The calculator applies the quadratic formula over the real numbers. You enter a, b, and c. The result is one or two real roots, or a clear stop when the discriminant is negative. The steps use the same substitution you would write on paper.
Equation ax² + bx + c = 0
Lesson: the real quadratic formula
The quadratic formula comes from completing the square on ax² + bx + c = 0, with a ≠ 0. The expression under the square root is the discriminant. A positive discriminant gives two distinct real roots. A zero discriminant gives one real root. A negative discriminant means the real square root is not defined, so this page does not invent a real answer.
This calculator does not factor by grouping and does not draw the parabola. It only evaluates the formula you see in the box.
Practice problems
1. Two real roots
Solve x² − 5x + 6 = 0.
2. No real root
Solve x² + x + 1 = 0 on this page, then open the Complex Roots Calculator.
Show answers
Problem 1. Δ = 1. The roots are 3 and 2.
Problem 2. Δ = −3. This page reports no real roots. The complex pair is −1/2 ± (√3 / 2)i.