Quadratic Formula Calculator
Solve quadratic equations of the form ax² + bx + c = 0 with detailed step-by-step solutions
Solve quadratic equations of the form ax² + bx + c = 0 using the quadratic formula with detailed step-by-step solutions.
Quadratic Formula Calculator
The calculator below solves the quadratic equation of ax² + bx + c = 0
Fractional values such as 3/4 can be used.
About the Quadratic Formula
The quadratic formula is used to solve quadratic equations of the form ax² + bx + c = 0, where a, b, and c are coefficients and a ≠ 0. It provides the solution(s) for x using the formula: x = (-b ± √(b² - 4ac)) / 2a.
The Formula:
x = (-b ± √(b² - 4ac)) / 2a
Discriminant:
Δ = b² - 4ac
• Δ > 0: Two real roots
• Δ = 0: One real root (repeated)
• Δ < 0: Two complex roots
Common Examples:
• x² + x + 1/4 = 0 → x = -0.5
• x² - 4x + 4 = 0 → x = 2
• x² - 5x + 6 = 0 → x = 2, 3
• x² + 1 = 0 → x = ±i
Applications:
- • Physics: Projectile motion
- • Engineering: Structural analysis
- • Economics: Profit optimization
- • Geometry: Area calculations
- • Finance: Investment analysis