The quadratic formula
x = (−b ± √(b²−4ac)) / 2a gives the two solutions of any quadratic equation.
Math calculators
Quadratic Formula Solver
Solve any ax² + bx + c = 0 — real or complex roots.
Complete guide
How to use Quadratic Formula Solver
Enter the three coefficients a, b, and c. The solver computes the discriminant (b²−4ac), determines whether the roots are real or complex, and returns both solutions plus the parabola's vertex.
When the discriminant is negative the roots are complex and are shown in a ± bi form. When it is zero there is one repeated root.
Reading the discriminant
Positive → two real roots; zero → one repeated root; negative → two complex roots.
Vertex of the parabola
The turning point is at x = −b/(2a), y = c − b²/(4a) — shown alongside the roots.
Answers
Quadratic Formula Solver FAQs
What is the quadratic formula?
x = (−b ± √(b²−4ac)) / 2a. It solves any quadratic ax² + bx + c = 0.
What does the discriminant tell me?
b²−4ac: positive means two real roots, zero means one repeated root, negative means two complex roots.
Can a be zero?
No. If a = 0 the equation is linear, not quadratic, and the solver shows an error.
What is the vertex?
The highest or lowest point of the parabola: x = −b/(2a), y = c − b²/(4a).
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