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