Solve quadratic equations in standard form and find the real or complex roots from the discriminant.
Last updated: June 2026 | By Patchworkr Team
The quadratic formula solves equations written in the form ax^2 + bx + c = 0. It is one of the most common ways to find the x-intercepts of a parabola.
The discriminant D = b^2 - 4ac determines how many solutions the equation has. Positive values give two real roots, zero gives one repeated real root, and negative values give two complex roots.
For x^2 - 5x + 6 = 0, the coefficients are a = 1, b = -5, and c = 6.
No. If a is zero, the equation is linear rather than quadratic.
It tells you whether the quadratic has two real roots, one repeated real root, or two complex roots.
Yes. When the discriminant is negative, the result panel shows the complex roots.
Yes. The calculator accepts decimal values for a, b, and c.
Related Tools
Solve absolute value equations.
Solve absolute value inequalities.
Apply associative property.
Multiply using box method.
Complete the square method.
Find complex roots.