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.