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Quadratic equation is a polynomial equation which is in the form of Ax$^{2}$ + Bx + C = 0 (second degree). Quadratic Equation Calculator (or Quadratic Equation Solver) is an online tool to solve a quadratic equation. If any quadratic equation is given then it can find factors of that equation, i.e. for the equation of the form Ax$^{2}$ + Bx + C = 0, it will find the values of x.

This calculator solves the quadratic equation with negative discriminant also, i.e. this calculator can find out imaginary roots (or complex roots) also.

## Steps to Solve the Quadratic Equation

Step 1 :

Observe the value of a, b and c from the quadratic equation.

Step 2 :

Find the value of discriminant(D) by applying the formula D = b2 - 4ac.

Step 3 :

If the value of discriminant is less than zero, write "roots does not exist/ imaginary. And if discriminant is greater or equal to zero, then find the roots of an equation by applying the formula x1= $\frac{-b + \sqrt{D}}{2a}$ and x2= $\frac{-b - \sqrt{D}}{2a}$

## Examples on Quadratic Equation Calculator

1. ### Find the roots of an equation x2 + 7x + 12 = 0?

Step 1 :

Here a = 1, b = 7, c = 12

Step 2 :

D = b2 - 4ac = 72 - 4 × 1 × 12 = 49 - 48

D = 1

Step 3 :

x1 = $\frac{-b + \sqrt{D}}{2a}$ = $\frac{-7 + \sqrt{1}}{2 × 1}$ = $\frac{-6}{2}$ = -3

x2 = $\frac{-b - \sqrt{D}}{2a}$ = $\frac{-7 - \sqrt{1}}{2 × 1}$ = $\frac{-8}{2}$ = -4

x1 = -3

x2 = -4

2. ### Find the root of an equation x2 + 4x + 5 = 0?

Step 1 :

Here a = 1, b = 4, c = 5

Step 2 :

D = b2 - 4ac = 42 - 4 × 1 × 5 = 16 - 20

D = -4

Step 3 :

Roots are imaginary, since discriminant is less than zero.