Quadratic Equation Solver
Enter coefficients for ax^2 + bx + c = 0 and instantly get the discriminant and roots. The solver handles real and complex solutions with precise formatting.
Enter coefficients for ax^2 + bx + c = 0.
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How quadratic equations are solved
A quadratic equation has the form ax^2 + bx + c = 0 with a not equal to 0. The quadratic formula gives the exact roots in terms of the coefficients.
The discriminant, D = b^2 - 4ac, tells you what kind of solutions exist. If D is positive, there are two real roots. If D is zero, there is one repeated real root. If D is negative, the roots are complex conjugates.
This calculator reports the discriminant and each root so you can quickly interpret the behavior of the parabola and its x-intercepts.
For large or small coefficients, rounding can matter. Use the precision setting if you need more decimal detail.