## ax2 + bx + c = 0

The quadratic equation solver is an online calculator to solve a standard quadratic equation.

As the name suggests, Quadratic equation solver solves any quadratic equation, which is in the form of ax2 + bx + c = 0, where a ≠ 0, using a Quadratic Formula.

By solving the quadratic equation, Quadratic Equation Solver arrives at values of x, for which the quadratic equation ax2 + bx + c = 0 holds true. This means, that when we replace x in ax2 + bx + c with the values calculated from quadratic equation solver, then ax2 + bx + c calculates to zero.

The simple formula to calculate the values of x for which ax2 + bx + c = 0 holds true, is called Quadratic Formula:

 Roots(x1, x2) = −b ± √   b2 − 4ac 2a

As you can notice in the formula. This implies, Quadratic formula calculates two values of x: x1 and x2, where

 x1 = −b + √   b2 − 4ac 2a

 x2 = −b - √   b2 − 4ac 2a

These two values of x for which ax2 + bx + c = 0 holds true, are called solutions of Quadratic Equation, also called roots of Quadratic Equation.

Nature of roots of Quadratic Equation

If b2 – 4ac > 0, then √b2 − 4ac  is real; hence we get two real and distinct roots.

If b2 – 4ac = 0, then √b2 − 4ac  is also zero; hence values of both x1 and x2 would be same and hence we get real and equal roots.

If b2 – 4ac < 0, then √b2 − 4ac  is imaginary number; hence we get imaginary roots.

If b2 – 4ac is a perfect square, then √b2 − 4ac  is a rational number; hence we get rational roots, else we get irrational roots.

How to use Quadratic equation solver

Step 1 - Convert the Quadratic Equation you wish to solve in Standard Form of Quadratic Equation, ax2 + bx + c = 0

For example, if you have a quadratic equation in the form of x2 - 6x = -8, then convert it into Standard Form of Quadratic Equation.

x2 -6x = -8 is converted into x2 - 6x + 8 = 0

Step 2 - Find value of coefficient a, b and c by comparing it with Standard Form of Quadratic Equation ax2 + bx + c = 0

For example, comparing x2 - 6x - 8 = 0 with ax2 + bx + c = 0, we get

a = 1,
b = -6,
c = 8

Step 3

 Roots(x1, x2) = −b ± √   b2 − 4ac 2a

 x1 = −b + √   b2 − 4ac 2a

 = −(-6) + √   (-6)2 − 4(1)(8) = 4 2(1)

 x2 = −b - √   b2 − 4ac 2a

 = −(-6) - √   (-6)2 − 4(1)(8) = 2 2(1)