# Quadratic Formula Calculator

## Calculator Use

This online calculator is a
**quadratic equation solver** that will solve a second-order polynomial equation such as ax^{2} + bx + c = 0 for x, where a ≠ 0, using the
**quadratic formula**.

The calculator solution will show work using the quadratic formula to solve the entered equation for real and complex roots. Calculator determines whether the discriminant \( (b^2 - 4ac) \) is less than, greater than or equal to 0.

When \( b^2 - 4ac = 0 \) there is one real root.

When \( b^2 - 4ac > 0 \) there are two real roots.

When \( b^2 - 4ac < 0 \) there are two complex roots.

## Quadratic Formula:

The quadratic formula

is used to solve quadratic equations where a ≠ 0 (polynomials with an order of 2)

### Examples using the quadratic formula

**Example 1:** Find the Solution for \( x^2 + -8x + 5 = 0 \), where a = 1, b = -8 and c = 5, using the Quadratic Formula.

The discriminant \( b^2 - 4ac > 0 \) so, there are two real roots.

Simplify fractions and/or signs:

which becomes

**Example 2:** Find the Solution for \( 5x^2 + 20x + 32 = 0 \), where a = 5, b = 20 and c = 32, using the Quadratic Formula.

The discriminant \( b^2 - 4ac < 0 \) so, there are two complex roots.

Simplify fractions and/or signs:

which becomes

calculator updated to include full solution for real and complex roots