The Quadratic Formula Solver is a powerful mathematical tool designed to find the roots of any quadratic equation in the form ax² + bx + c = 0. Whether you are dealing with real or complex roots, this solver provides a comprehensive step-by-step breakdown of the derivation process, making it an essential E-E-A-T verified resource for students and educators.

Primary Formula

x = (-b ± √(b² - 4ac)) / 2a

schoolStep-by-Step Worked Example

Solve for x: 2x² - 4x - 6 = 0

Identify coefficients: a = 2, b = -4, c = -6
Calculate the discriminant (Δ = b² - 4ac): (-4)² - 4(2)(-6) = 16 + 48 = 64
Apply the formula: x = (4 ± √64) / 4
Simplify: x = (4 ± 8) / 4
Find the roots: x₁ = 12 / 4 = 3, x₂ = -4 / 4 = -1

The roots are x = 3 and x = -1.

helpHow to Use

1
Enter the coefficients a, b, and c from your quadratic equation.
2
Click "Calculate Roots" to evaluate the equation.
3
Review the discriminant (Δ) to understand the nature of the roots.
4
Follow the step-by-step breakdown to see exactly how the quadratic formula is applied.

forumFrequently Asked Questions

What is the quadratic formula?

The quadratic formula is a closed-form expression used to find the solutions (or roots) of a quadratic equation of the form ax² + bx + c = 0.

What does the discriminant tell us?

The discriminant (b² - 4ac) indicates the nature of the roots. If Δ > 0, there are two real roots. If Δ = 0, there is one real root. If Δ < 0, there are two complex roots.