Math
Solve ax² + bx + c = 0
Enter coefficients a, b, c to find both solutions. Shows discriminant, vertex, and factored form.
In this article
The Quadratic Formula
x = (-b ± √(b²-4ac)) / 2a solves any equation ax² + bx + c = 0. The ± gives two solutions. The discriminant (b²-4ac) determines the root type: positive = 2 real roots, zero = 1 repeated root, negative = 2 complex roots.
The Discriminant
The discriminant tells you everything before solving. b²-4ac > 0: Parabola crosses x-axis twice. = 0: Touches x-axis once (vertex). < 0: Never crosses x-axis (complex roots).
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Frequently asked questions
What is the quadratic formula?▾
x = (-b ± √(b²-4ac)) / 2a. Enter a, b, c and get both solutions. Example: x²-5x+6=0 → a=1, b=-5, c=6 → x=3 or x=2.
When are there no real solutions?▾
When b²-4ac is negative — the square root of a negative requires imaginary numbers. The parabola never crosses the x-axis.
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