Quadratic Equation Solver
Find roots of quadratic equations ax² + bx + c = 0. Fast, free, and fully client-side.
Calculator Inputs
How the Quadratic Equation Solver Works
A quadratic equation solver calculates the roots of second-degree polynomials of the form ax² + bx + c = 0. Depending on the discriminant value (b² - 4ac), the equation produces two real roots, one repeated real root, or two complex conjugate roots.
Formula
x = (-b ± √(b² - 4ac)) / (2a)
The discriminant Δ = b² - 4ac indicates real roots if Δ ≥ 0, or complex roots with imaginary unit i if Δ < 0.
Calculation Example
For x² - 5x + 6 = 0 (where a=1, b=-5, c=6): Discriminant is 25 - 24 = 1, yielding roots x = (5 + 1)/2 = 3 and x = (5 - 1)/2 = 2.
Frequently Asked Questions
What does a discriminant of zero mean?
It means the parabola touches the x-axis at exactly one point (a single repeated real root).
Can the coefficient a be zero?
No, if a = 0, the equation reduces to a first-degree linear equation (bx + c = 0).