There are many cases where the resolution of a quadratic equation by factoring or completing the square is not easy because it requires a lot of handling. In these cases, quadratic formula is quite useful and time saving way to solve the quadratic equations.

As we know a quadratic equation is an equation of the form ax2 + bx + c = 0 where a, b, and c are constants and a ≠ 0

 Roots(x1, x2) = −b ± √   b2 − 4ac 2a

Step by step process to solve the quadratic equation by quadratic formula:

Step I: Arrange the Quadratic Equation in the standard form of ax2 + bx + c = 0.

Step II: Compare the quadratic equation which is to be solved with the standard form of quadratic equation and find out the values of the coefficients a, b, and c.

Step III: Put these values of a, b, and c in 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, or roots of Quadratic Equation.

Example: Solve, x2 - 10x = -24

Step I: - Convert above equation in standard form of quadratic equation, ax2 + bx + c = 0

x2 -12x = -32 is converted into x2 - 12x + 32 = 0

Step II: - Now find the value of coefficients a, b and c by comparing it with standard form of quadratic equation ax2 + bx + c = 0

Comparing x2 - 12x + 32 = 0 with ax2 + bx + c = 0, we get

a = 1,
b = -12,
c = 32

Step III: Putting values of a, b and c in the quadratic formula

 Roots(x1, x2) = −b ± √   b2 − 4ac 2a

 x1 = −b + √   b2 − 4ac 2a

 = −(-12) + √   (-12)2 − 4(1)(32) = 8 2(1)

 x2 = −b - √   b2 − 4ac 2a

 = −(-12) - √   (-12)2 − 4(1)(32) = 4 2(1)

8 and 4 are the roots of the quadratic equation x2 -12x = -32