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Quadratic Equation Solver
Roots, discriminant and vertex for any quadratic equation. Everything happens on this page, in your browser — nothing you enter is sent anywhere.
For an equation written as ax² + bx + c = 0, type the three coefficients:
The discriminant (b² − 4ac) decides the shape of the answer before you compute anything: positive means two crossings of the x-axis, zero means the curve just touches it, negative means it never reaches it in real numbers.
How this tool works
A quadratic equation hides three answers inside its coefficients: where the curve crosses the axis (the roots), whether it crosses at all (the discriminant), and where it turns (the vertex). This solver reports all three, because exam questions ask for all three — rarely in the same breath.
Using it, step by step
- Rewrite your equation so everything sits on one side and zero on the other; read a, b and c off in x², x, constant order.
- Type the coefficients, watching the signs — a subtracted term means a negative coefficient.
- Read the discriminant first to know how many real roots to expect, then the roots themselves.
- Check a root by substituting it back into the original equation; it should give zero, or very close with rounding.
Where it stops
Roots are printed to four decimal places, which is plenty for school work but is rounding nonetheless. If your course expects exact surd form, use the discriminant and the quadratic formula by hand — this page's decimal is then a checking device, not the answer.