Quadratic Formula Calculator

Solve quadratic equations of the form ax² + bx + c = 0 with detailed step-by-step solutions

About the Quadratic Formula

The quadratic formula solves equations of the form ax² + bx + c = 0, where a ≠ 0. The formula x = (-b ± √(b² - 4ac)) / 2a provides the solution(s) for x.

The Formula:

x = (-b ± √(b² - 4ac)) / 2a

Discriminant (Δ):

  • • Δ > 0: Two real roots
  • • Δ = 0: One repeated root
  • • Δ < 0: Complex roots

Examples:

  • • x² - 5x + 6 = 0 → x = 2, 3
  • • x² - 4x + 4 = 0 → x = 2
  • • x² + 1 = 0 → x = ±i

Applications:

  • • Projectile motion
  • • Structural analysis
  • • Profit optimization

Quadratic Equation: ax² + bx + c = 0

Fractions like 3/4 are supported

Solution Steps

Enter coefficients and click Calculate to see the step-by-step solution