Quadratic equation solver
Enter a, b and c. Get the roots — including complex ones — plus the discriminant and vertex.
- Runs in your browser — nothing you enter is uploaded
- No sign-up, no quotas, free to use as often as you like
How it works
The quadratic formula is easy to write down and easy to get wrong under time pressure, usually through a sign. This applies it exactly and shows the discriminant, which is the part that tells you what kind of answer to expect before you have it.
The discriminant tells you the shape of the answer
b² − 4ac decides everything. Positive means two distinct real roots and a parabola crossing the axis twice. Zero means one repeated root and a parabola touching the axis. Negative means no real roots and a parabola that never reaches the axis — the solutions are a complex conjugate pair, which this tool gives you rather than reporting an error.
Complex roots are shown properly
Many solvers refuse when the discriminant is negative. The roots exist; they are simply not real. They are given here in the form p ± qi.
Vertex and axis of symmetry
The turning point and the vertical line the parabola is symmetric about, both of which come straight out of the same coefficients and are usually what a graphing question actually wants.
When a is zero
The equation is not quadratic at all but linear, and the single root is given with a note saying so, rather than dividing by zero.
Quadratic equation solver — questions
What does the discriminant tell me?
Whether there are two real roots (positive), one repeated root (zero) or a complex conjugate pair (negative).
Does it handle complex roots?
Yes, given as p ± qi rather than refused.
What if a is zero?
The equation is linear. The single root is calculated and labelled as such.
Does it show the working?
It shows the discriminant, roots, vertex and axis of symmetry, which is the substance of the working.
Is anything sent anywhere?
No. It is solved in your browser.