Quadratic Formula Calculator

Use this Quadratic Formula Calculator to solve equations in the form ax² + bx + c = 0. It calculates the roots, discriminant, vertex, and axis of symmetry.

Calculation Method

Quadratic formula:

x = (−b ± √(b² − 4ac)) ÷ 2a

Discriminant:

D = b² − 4ac

• D > 0: two real roots
• D = 0: one repeated real root
• D < 0: two complex roots

The x-coordinate of the vertex and axis of symmetry is:

x = −b ÷ 2a

Example

Solve:

2x² + 5x − 3 = 0

First calculate the discriminant:

D = 5² − 4(2)(−3) = 49

Then:

x = (−5 ± √49) ÷ 4

The roots are:

x = 0.5 and x = −3

Important Note

The coefficient a cannot be zero. If a = 0, the equation is linear rather than quadratic. Long decimal results may be rounded for display.

Source

• OpenStax Intermediate Algebra — Quadratic Formula