Quadratic Equation Solver
Solve quadratic equations of the form ax² + bx + c = 0. Find real and complex roots with step-by-step calculation details.
Equation Parameters
ax² + bx + c = 0
Coefficient of x² (must not be zero)
Coefficient of x
Constant term
Solution
Enter coefficients and click Solve
About Quadratic Equations
A quadratic equation has the formax² + bx + c = 0
, where a ≠ 0.
Root Formula
x = (-b ± √(b² - 4ac)) / 2a
Discriminant
D = b² - 4ac
- D > 0: Two distinct real roots
- D = 0: One root (two equal roots)
- D < 0: Two complex conjugate roots
Examples
- x² - 5x + 6 = 0 → a=1, b=-5, c=6 → x₁=3, x₂=2
- x² - 4x + 4 = 0 → a=1, b=-4, c=4 → x=2 (double root)
- x² + x + 1 = 0 → a=1, b=1, c=1 → complex roots