Quadratic equation solver
Enter a, b and c of ax² + bx + c = 0 and get the solutions with every step: the discriminant, the quadratic formula, the vertex of the parabola and, where possible, the factorised form.
For ax² + bx + c = 0.
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How it's worked out
How it works
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
The quadratic formula
x = (−b ± √D) / 2a, where the discriminant D = b² − 4ac.
- D > 0: two real solutions (the parabola crosses the x-axis twice).
- D = 0: exactly one solution (the vertex touches the x-axis).
- D < 0: no real solutions, but two complex ones, such as 1 ± 2i.
For x² − 5x + 6 = 0: D = 25 − 24 = 1, so x = (5 ± 1) / 2, giving x = 2 or x = 3, and the factorised form is (x − 2)(x − 3).
a = 0?
Then it isn't a quadratic equation but a linear one, bx + c = 0, and the calculator solves that instead. For several equations with several unknowns, use the system of equations solver.
Frequently asked questions
Is the quadratic equation solver free?
Yes. The quadratic equation solver is completely free, with no account, sign-up or usage limit.
How accurate is the result?
The tool calculates with your browser's number precision. For important calculations, always double-check what you entered.
Does it work on my phone?
Yes. The tool works in any modern browser on a phone, tablet or computer.