Equation Solver
Free equation solver. Solve linear equations (ax + b = 0) and quadratic equations (ax^2 + bx + c = 0) with the quadratic formula, showing the discriminant, roots, and a complete step-by-step solution.
Enter the coefficients of the equation ax² + bx + c = 0
How to Solve Quadratic Equations
A quadratic equation has the form ax² + bx + c = 0, where a ≠ 0. It is solved using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. The discriminant (b² - 4ac) determines the nature of the roots.
The Discriminant
If Δ > 0: Two distinct real roots. If Δ = 0: One repeated real root. If Δ < 0: Two complex conjugate roots.
Frequently Asked Questions
What is the vertex of a parabola?
The vertex is the highest or lowest point of the parabola. It is calculated as: x = -b / 2a, y = f(-b / 2a). If a > 0, the vertex is a minimum; if a < 0, it is a maximum.
Do all quadratic equations have solutions?
Yes, every quadratic equation has solutions in the complex numbers. If the discriminant is negative, the roots are complex (they have an imaginary part).