Learn How to Solve Quadratic Equation – Factorization or Equation Calculator

Most basic question is what is quadratic equation? The answer is, any algebraic equation having degree two with its coefficient, is called quadratic equation.  The quadratic equation is one of the most complex equations of the mathematics where a student feels complexity in solving them. It is easy to solve any linear equation, but it is quite tough to solve an equation with a higher degree.

Quadratic Equation
Quadratic Equation

How to solve quadratic equation?

To solve any quadratic equation there are two methods one is the most basic method which is also known as formula method, another method is directly used quadratic equation calculator.

Method-1: Factorization

Firstly, let us discuss basic method which is quite easy to understand.

The standard form of quadratic equation is –


Let us consider an example, a.) x² + 4x +3=0

Apply basic factorization method to solve this equation.

Step-1) x(x+3) +1(x+3)

Step-2) Arrange common terms together

Step-3) (x+1) (x+3)

Step-4) x=-1 or -3

For better understanding, let us consider another example, b.) x2+5x=0

Step-1) take x in common

Step-2) x(x+5) =0

Step-3) x=0 and x+5=0

Step-4) x=0 and x= -5

Therefore, x has two values, x=0; x= -5

Method-2: Quadratic equation calculator

Now, we discuss another formula to solve quadratic equation, which is known as quadratic equation calculator.

To solve the quadratic equation, the algebra calculator uses a genuine method or use a formula to identify values of a variable. The formula for solving quadratic equation is

x= (-b±√ (b²-4ac))/2a

Let us consider an example,

x2 + 4x +3=0

So, here a=1, b=4, c=3, now put all these values in the above equation, then solve it.

Therefore, you got two values of x, x= -1 or x= -3.

It is a direct formula-based method, or the digital calculator offers their users to solve any of the quadratic equations with the formula method. That means you can learn how to solve any quadratic equation with the formula method. In the calculator, you just need to enter the question in the required field. Different signs, roots, square root, and mathematical signs are available on the platform. Thus, you can enter the quadratic equation to solve it and find its variable values. According to the degree available in the unknown term, you will get values accordingly.  Now a day, the quadratic equation is also available on the internet where one can direct put values in the given space and then click on the submit button to get the final value of your required coefficient.

Here, you can choose the algebra calculator that can easily find out variable values and deliver results in fast. In the algebra calculator, you just need to enter the quadratic equitation on the required field in the calculator. Thus, enter one next tap to solve the equation. The calculator solves the equation with the genuine method, and there is no short answer you will get. Thus, solving quadratic equations is quite easy with the calculator as compare to factorization method. Factorization method sometimes fails in solving an algebraic method only when the equation is of higher degree, which makes the solution too much complicated. In that case, quadratic equation calculator method is beneficial for the user.

If someone is comfortable in factorization then apply, factorization method to solve quadratic equation otherwise use easy to implement a method which is quadratic equation calculator.


A Brief Introduction to Quadratic Equation


Do you know about Quadratic equation? If your answer is “No” Then we will tell you the answer. A quadratic equation is an algebraic equation where coefficients with a degree of two or more. A standard quadratic equation contains only the powers of a coefficient of X, which are non-negative. But how to solve these equations, if you are unaware then here is the way. After this, you will be able to solve any question of quadratic equations.

How to solve a quadratic equation?

To know the exact method to solve the quadratic equation, read this article. Consider an example of a quadratic equation which helps you to understand their solution

x2 – 5x = 6

The standard format of quadratic equation is-

ax2 + bx + c = 0

According to the standard format of quadratic equation, the given an example is not as the standard format. Thus, you need to make the R.H.S. is equal to zero of the above example. You will get-

x² – 5x – 6 = 0

The standard format of quadratic equation, you have

a=1, b=-5 and c=-6

To solve the given quadratic equation, you need to use the Quadratic formula calculator that can help you to perform complex mathematical operations easily. The quadratic formula is

x = (-b±√ (b²-4ac))/2a

The quadratic equation solver teaches you to solve any problem. Once you entered the problem into the required field in the calculator, it explained each step of the quadratic solution. In the solving process-

Puts the values in the quadratic formula

x = (-(-5)±√(25+4.1.6))/2.1

x = (5±√ (25+24))/2

x = (5±√49)/2

x = (5±7)/2

Now, you have the result of the given problem. In the quadratic equation, there are two results you can find that means; you will get two factors for a single variable. So, you need to separate ± signs and find both values of a variable.

If you consider positive sign then the answer will be:

x= (5+7)/2



If you consider negative sign then the answer will be:

x= (5-7)/2

x= (-2)/2


Now, you have two values for single variable, i.e. x=6 and-1. Therefore, X=6 and -1.

The algebra is the most important branch of mathematics that includes the higher degree of at least one coefficient. The higher degree of the coefficient in the equation improves the complexity of the equation which becomes a nightmare for the students. A Linear equation is quite easy to solve, but any equation with the higher order of degree is too difficult to solve. For solving such kind of equation, one can also use quadratic equation calculator, for instant results without any complex calculations.

The digital calculator offers their users to solve any of the quadratic equations with the formula method. That means you can learn how to solve any quadratic equation with the formula method. In the calculator, you just need to enter the question in the required field. Different signs, roots, square root, and mathematical signs are available on the platform. Thus, you can enter the quadratic equation to solve it and find its variable values. According to the degree available in the unknown term, you will get values accordingly.

For example- In a linear equation, there is single degree available in the variable thus you will get one answer for the unknown variable. On the other hand, the quadratic equation includes 2nd order degree that delivers two values of unknown.

If someone is comfortable in factorization then apply, factorization method to solve quadratic equation otherwise use easy to implement a method which is quadratic equation calculator.

Solving the Quadratic Equation


In the wide varied domain of algebra, we come across various kinds of math problems involving the need to solve them. These things termed as equations are further classified into multiple parts. Some of them are Linear equations, Quadratic equations, Cubic equations, and Polynomials.

An algebraic equation with the maximum order of the variable being two is a quadratic equation.

Let us start with understanding the form of the quadratic equation.

Something of the form ( ax2 + bx + c = 0 )is a quadratic equation.

Here the letters a,b and c are the coefficients of the equation.


It is important to know what exactly the solution of an Algebraic equation means.

To find the solution of an equation, we equate the function or the equation to zero and further solve with respect to that condition. Now that we have known what a solution means in the mathematical terms

Let us know how to find the solution.

The solution of a quadratic equation can be found out using three methods, which are listed below.

  1. Factorizing the Equation

The very first method is the factorizing method. It is the most used and easiest way to get the solutions in a very accurate and reliable manner.

Let us know what factorizing is:

It is basically about dividing the coefficient that belongs to order one, into products of two numbers such that it is equal to the coefficient of the 1st order of the variable. It is a very useful skill that is applicable in many algebraic problems.

After separating the numbers, present them using the distributive property of multiplication which is of the form (x+a)(x+b) where a,b, can be any numbers and x is the variable.

Once you have learned the art of factorizing, the further processes are very basic and trivial. Now to find the solution, as previously discussed, equate each bracket (x+a) and (x+b) to zero. You will find the values of x in terms of the solutions as –a and –b respectively.

This can be further mastered by practicing a small problem set of examples.

  1. The Quadratic Formula

You can always try for the factorizing way first, but if in case you are stuck somewhere or if the factorizing gets tough, or the answers are complex, you have no choice but to remember this method. No worry, it isn’t a huge gigantic formula but a little act of remembrance that will help you lifelong in solving quadratic equations. This is the most effective way that will surely lead you to the right answer.


Here the value (b² – 4ac) is the discriminant. This value of the discriminant further helps to categorize the nature of the roots.

If the value of the discriminant is positive, then the equation has 2 real solutions, if the value of the discriminant is zero, then the equation has one real and one complex solution. If the value of the discriminant is negative then both the roots are negative.

Even if you use the factorizing way but aren’t sure about your answers, you can give this method a try, just to verify your derived answers. It is very beneficial in solving large and complex equations.

  1. The Smart Calculator

Nowadays, you do not have to worry if you mess up with a few steps. If you still do not feel confident about the answer, give the computer processor a try! Try solving the problem using an Algebraic calculator, and you no more need to verify it!

Getting difficulty in Solving Polynomial Expression, Use Online Math Software

Are you a high school student? Then definitely you have some favorite subjects, it could be science, mathematics, English or any other. Learning your favorite subjects will not make you stress, and you are always ready to study it. Learning them is fun and exciting, and you never feel bored. Not all subjects are interesting, and mathematics is not the favorite of many students. It is not tough when you are in the lower grade, but as you move to the higher class, you have to solve difficult problems like polynomials, algebra and multiplying fractions.


Many students face difficulties in explaining them, and that’s why their parents hire tutors. But hiring a tutor is not the best option because he will also teach the same way the student learns in school. Spending extra hours in learning mathematics will help you, but what if you are stuck in between solving the problem and there is nobody to help you at that moment. At that time you can take help of online math software that can solve complicated equations within seconds. This software is useful for students and helps them in examinations.

What can you do with online math software?

  • Students can solve any algebra problems; solve any polynomials expression, etc.
  • Learn step by step operations to solve the equations. Simplify each problem in straightforward ways that even a weak student can understand it.
  • Students can see the online demo and watch the tutorials according to topics. All the topics are listed in the table and students can watch the latest and previous solved questions by watching videos.
  • While solving any equation say polynomials expression you stuck at any step then use the online software. Just enters the whole expression and press simplify to get the solution.
  • Learn how to apply the rules to solve the particular problem.

Taking help of internet in studies is a very good option because there you will get interesting ways to learn the difficult topics. Mathematics is one of the most difficult subjects for most of the students. And this software makes the learning fun and makes students understand difficult questions in the very easy way. This software is easy to use, and the answer and explanations they provide are accurate and exact. Therefore if you are weak in mathematics, then you must take help of this software. It has many benefits and here are few of them.

The Benefits of using math software to solve polynomial expressions-

  • Accuracy- software is well programmed, and hence it can accurately solve any mathematical questions. You can rely on its answer and if you have doubt then compare the solutions provided by the teacher.
  • Solve any problem– online math software can answer any questions like algebra, HCF, LCM, polynomials, matrices, etc. Students can answer any topic of mathematics with accuracy using this software.
  • Anytime- your teacher can’t help you every time. Once you reach home and you do not have any elder person to assist you in mathematics then this software can help you.

Online math software is thus very useful for students who have opted mathematics stream to solve simple polynomials problems form tough ones.

How students can learn to solve Algebra problem

Algebra is known as a gatekeeper subject because it has importance in different fields which are not related to math. Algebra brings in alphabets and numbers, and they are combined in an equation.

For the students to be able to solve the algebra problem, they will have to be accustomed to abstract thinking required by algebra, or it will continue to be an elusive part of math. The researchers and educators do attach a large importance to the algebra.   It is considered to be the real math that the students normally learn. It is not clear at which time that the students will have to be introduced to the real math. Some students start to learn algebra early, but others do maintain that the students should wait to start learning algebra.


Even if the debate continues, a number of the researches had found out that students do poorly in the algebra and they do not improve their grades.  Some students are interested in algebra from the start but others try their best to avoid this subject, and they put it off up to the time they cannot avoid it anymore.  It is easy to learn algebra when the students are given step by step instructions. They do allow them to understand every step in solving methodology.

Algebra word problem is what many students may find hard. The word problem gives too much information, and it gives the clear idea of what someone has to find and what you have to base yourself on.  The first step in solving algebra problem is to understand the algebra terminology.

The students do not have to memorize many equations of algebra. Learning formula, writing them down and to work on them, helps to understand more on how to solve algebra problems. You cannot learn algebra through reading only, but you can get paper and pencil ready to start working. Practicing should not be negotiable. You can start using simple problems and then move to even complicated problems. You should try to work on many problems using different sources.  You should not base yourself on the handouts, text books, and class notes.

To solve the algebraic problem, you have to remember that there are two sides in the equation. An equal sign is to divide an equation at the right and left a side. When the problem has no equal sign, then you cannot solve to get the variable, but you only need to simply such problems.

To solve the algebra problem, you will need to take the following steps:

  • You have to look for distributive property and then to solve the problem. You will need to pay attention to the signs used.
  • You should combine the numbers that look the same on one side before you can use simply everything
  • You should subtract or add an inverse operation, get the variables at one side of and then the integers at the other side.
  • The final step should be to isolate the equation at one side and solve the equation on its own.
  • After getting the variable, then you have to use the substitution in order to check for the answer.

How to Solve Quadratic Equations

The equation is most of the time used when it comes to solve some practical problems.  When it comes to solve quadratic equations, you will need to know the steps that are involved in coming with the right answer.

First, you will need to read a problem given in a careful manner and to note down what should be done.

Choose the letter or the letters that have been used to represent unknown quantity

Represent a word statement of a problem in the symbolic language step by step

Consider the quantities that are equal according to the conditions that were given and the form of an equation or equation.

Quadratic Equations
Quadratic Equations

You can then solve the equation that you got in the fourth step.

Check the results if you want to ensure that the answer had satisfied the requirements of problems.

An expression which is written as ax2+bx+c=0 is the quadratic solution but a should be different to zero. The equation is also called standard or general form. It is possible to solve the quadratic equation by using the formula or by factorization. The formula is to get the root for the quadratic equation, and it is as follows.

Now it is easy to solve the applied problems because of the wide variety of the applied problems. You cannot find any single technique to solve the equation in every case.

If you find problems with solving quadratic equations, then online tutor is the right way to go. The tutor offers the best way to deal with the math problems.  Many students have a problem in math while there is always an emphasis on getting good grades to get job placement. Math tests at the metric measurement are an example of the terrible anxiety, and many students will not have any choice but getting the help needed so that they may gain their confidence.   The tutor will develop the learning process and will develop a customized instructional program.

The tutor helps the student to learn how to sit and to receive the individualized instruction about the work, and they may be having trouble like with metric conversion calculator. There is no learning curve that can be the same as that of someone else.

If you want to find a tutor, then you can ask for the recommendation from family or friends who may be aware of the tutor.  The school can also recommend a tutor according to the subject they are teaching and the help the student can get. Most colleges may post the available tutors at their notice board. Some teachers and retired teachers can offer the tuition in order to make money.

If you are looking for the tutor to help you into solve quadratic equations, you will need to check if he has enough experience and professional training.  You also have to know if he is capable of offering the service depending on the level of difficult you have.  The job of the tutor will teach you the concept and the strategies of problem-solving for equations.

How to Solve Quadratic Equations within a minute without a Calculator?

A quadratic equation is the branch of algebra which is the important part of mathematics. It includes three important terms as variable, content, and coefficient. Before going to solve the equation without greatest common factor, you need to know some basics about the algebraic expression. The quadratic algebraic equation includes 2nd order degree on the variable. Hence, there are two values you can find for a variable. Consider an example as mx² + nx + p = 0

Here some of the common term as

Variables: Variables are the term whose value varies with constant and coefficient available in the mathematical expressions. Here ‘x’ is the variable in given equation.

Constant: Constant value is the numerical value or number available in the equation which cannot be changed. In the above equation, the ‘p’ is the constant value.

Coefficient: in the term of any algebraic equation, a coefficient is also the numerical value. In the given standard quadratic equation’ and ‘n’ are coefficients.

How to solve the quadratic equation without a calculator?

Consider examples to solve the quadratic equations without using the calculator and formulas.

x² + 5x + 6 = 0

x² – 5x + 6 = 0

x² – 5x – 6 = 0

x² + 5x – 6 = 0

There are four quadratic examples, and it can be solved without the formula method. It is easy when you have great skill in mathematical calculation.

For first equation to solve it- 

x² + 5x + 6 = 0

First, you have to choose the right factor. For this, you have selected the coefficient of x² and constant value. After getting factors, you need to make set where the sum of these is equal to the coefficient of ‘x.’ now divide both the factors by the coefficient of x² . And the most important (+, +) signs make (-,-) in the result.

For above equation, factors are 1 and 6, and 6 can be factored as 2 and 3. The multiplication of 2×3 is equal to 6 and the sum of 2+3 = 5. So we get 2 and 3 as a result.

For second equation

x² – 5x + 6 = 0

We have (-, +) signs on the quadratic equation. The factors are 2 and three as identified above in the expressions. So, the signs provide (+, +) signs on the result. Now the equation provides two values as (3, 2).

For third equation

x² – 5x – 6 = 0

There are (-, -) signs are available which provide (+,-) signs on the result. The factors are 2 and 3 for the above equations. Keep the thing in mind that the first sign is for big numerical value. Now the value of ‘x’ is (3, -2).

For fourth equation

x² + 5x – 6 = 0

In algebra problem there are (+,-) signs which provide (-, +) signs in the result. And the first sign is always for the big numerical value. Now the equation provides (-3, 2) values for ‘x.’ in this method, dividing fractions is a difficult task. Also, you can experience the decimal to fraction and fraction to a decimal operation to make the complex equation simple.

Instead of this short method, the formula can be used.


This is also the easiest method to solve quadratic equations, but some mathematical calculation makes it difficult.

Pick up the Best Method to Solve Quadratic Equation

There are many interesting facts and lessons that you may get to witness in mathematics. You may get to experience some of the best ones in the algebraic portions. Algebra stands to be one of the most important parts of mathematics and has many interesting things for the learners. Quadratic equations being some of the complex algebraic problems, there are many who find some better ways to solve quadratic equations. Equations are not so difficult if you relate the various components in it with something easier. You may see that these are just like the fill in the blocks exercises that you solved in the childhood.

Quadratic Formula
Quadratic Formula

Quadratic Equation – its complete meaning

An equation can be said to be any algebraic expression that is stated in the form of ax²+bx+c = 0

is known as a quadratic equation. Here, a, b, and c are known to be constants, and “x” is the variable. Therefore solving such complex equations may involve some specific methods and essential steps to be performed. These are a bit more complex than linear equations, therefore, you need to move out to advanced learning and solving strategies. There are many different methods that you can use to solve equations like this. There are both advantages and disadvantages related to the use of these methods. Considering these will help you to get the correct answers more easily.

Know the various methods

There are many ways in which you can bring out the correct answers fir the value of “x” in the quadratic equations. Knowing the best one will help you to complete algebra homework on time. Therefore here are the methods used to solve quadratic equations:

Completing the Square: This is usually a process including multiple steps. In this method, the main motive is to convert the quadratic in the form of (x+a)² = b

  • The condition here remains the same,e., and b are constants. This method is the best to give perfect insights of the working of algebra. Also, this method is known to bring the correct answers always which are the advantage of using it. However, the disadvantage with it is the complexity it may involve.
  • Factoring: the factors of any quadratic equations will be said to be (max + r)
    and (nx + t). However, you will be able to find the correct answers only when the solution is an integer. Non integer solutions will not be found with this method which constitutes to its disadvantage. This method can be performed really faster, and it is the advantage with it.

Quadratic Formula: the formula is stated as:  -b±√b²-4ac ⁄ 2a the quadratic formula is designed in a way that it reduces the complex steps that are involved in solving a quadratic. This makes it straightforward which is the advantage. However the technique can turn out to be rote constituting to be the disadvantages.

Thus you can make use of these methods to complete your algebra homework. Though these are a bit complex than linear equations, you can make use of the simplest and the best methods. These will help you to solve quadratic equations and get the correct solutions.

How to Simplify System of Equations

There is a linear and nonlinear system of equations. The latter being a set of simultaneous equations whereby the unknowns appear as variables of a polynomial of degree higher than one in the argument of a function which isn’t a polynomial of degree one. Nonlinear equations are not always easy to deal with. Quadratic equations are examples of nonlinear equations. In short, a system of equations is a set of equations that are dealt with all together at a go.

Since solving these equations isn’t always a walk in the park, some guys decided to come up with a desktop application that simplifies them. They are called softmath, and they are based in the US. They called that app “Algebrator”.

How does algebrator work?

First of all, it can be downloaded through the link that is provided on their webpage softmath.com. As of now, its cost is roughly ten bucks. But, that is bound to change in the next few hours. So if you feel like purchasing it after paying attention to what it does, I would advise you to do that sooner rather than later.

Now, let us dive deep into Algebrator. This solution tackles problems from many math textbooks. It tackles those that are in Trigonometry, Statistics, Pre-Algebra, and College Algebra. Imagine it can solve problems from the following topics; complex numbers, graphing, trigonometry, equations, and inequalities, logarithms, functions, math expressions to name but few. Is that not great? I bet it is.

The app allows the use of wizards interface or WYSIYWG interface (an acronym of What You See Is What You Get interface) to enter problems like “Find a perpendicular line that passes the (x, y) coordinates”.

With this app, you can ask for the explanation of something if you did not get how it arrived at that place. Just like how the teacher shows his or her steps while calculating something, this application will do the same too. That way, it makes sure that you have understood how it some things are done.

When you get the solution, you can export it in MathML format. If you do not mind, you can go ahead and share that solution with your friends or classmates or even everyone. The application has an export function which generates xhtml files which can be easily opened in web browsers like Google Chrome, Mozilla Firefox, Internet Explorer, Microsoft Edge, Safari, Opera and many more.

Who can install this application?

As of now, the app can be installed on Windows PCs or Mac OS laptops.

Do they provide customer support service?

Yes, they do. Softmath provides customer services every week day from 8 o’clock in the morning to 9 o’clock in the evening. They can also be reached through the phone call using the number that they have indicated in their webpage.

If you prefer having a one on one talk, you can get them at their office which is located along Blanco Road in the city of San Antonio in the State of Texas.

Know dividing polynomials with small example to understand better

dividing polynomials

Dividing polynomials is not an easy task as it seems. Sometimes the polynomials equations include higher degree that is why it is difficult to solve it. Basically, the polynomial equation is same as the algebraic or the quadratic equation. But the major difference between both is the algebraic equation does not contain degree on variables, but quadratic includes it. The polynomial equation usually contains same variables in the quadratic form. To better understand consider an example which is suitable-

3a + 2b = 18 algebraic equation

x²+2x+ 8=0 Polynomial equation

When you are dividing polynomials, and then feel some difficulties. Due to lack of knowledge of mathematics operation and the complexity of polynomial; makes it more difficult. The variables include different values that are why it is hard to solve. There is no direct method to solve polynomial equations.

When you are looking for understating the dividing the polynomial consider an example.


This is divided by


The dividing rule is same as we have performed in previous classes. But the variable in dividing polynomials makes complexity in solution.

Take the figure in this form as below



To solve this polynomial determine the degree of both the equation. As shown in the first equation has 3 higher degrees and the second includes one.

In the first step of division, to need to divide first equation by     x²

We take x² because it can eliminate the (x³) from the equation. In a first step, we can eliminate the higher degree than we go to the lower degree.

After division we have,


Now you have to follow the second step in which, the elimination of second-degree performs. Divide the equation with ‘5x’ that can help you to eliminate the term 5x².

Now we have taken 5 with the variable it is done to eliminate both x² and 5 from the equation. After dividing the above equation, you will get,


Now we have eliminated the first and second degree. Now you have to eliminate the variable which includes a single degree. For this purpose, we need to repeat the previous step with different numerical values. Divide the above equation by (x-2) with (-3)’s multiplication. This will help you to eliminate (-3x) from the equation.

After division, you have 0 remnants. So, keep the numbers which are multiplied by the divider. Above we used

x² , 5x and -3

We need to add these results to get the final answer.

Hence the solution of this equation is

x²+5x -3

Basically, it is not difficult to solve the equation, but it needs huge grip in a calculation, division, multiplication and much more. Also, it needs great basic knowledge of mathematics for dividing polynomial. In the current, the polynomial equation is taken to know the intelligence of people. That is why it is used in many competitive exams. It makes the brain exercise perfect and helps to master in a calculation. It is beneficial for us so, we need to practice more and more to understand the division polynomial. After regular practice, you can become a master in it.