Quadratic Equation Solver

Quadratic Equation Solver takes the coefficients of ax2 + bx + c = 0 and returns the roots, together with every step of the working rather than just the answer.

The solution comes from the quadratic formula, x = (-b plus or minus the square root of (b2 - 4ac)) / 2a. The expression under the root is the discriminant, and it decides the shape of the answer before you calculate anything: positive gives two distinct real roots, zero gives one repeated root, and negative gives two complex roots. The calculator reports the discriminant first and says what it means, because that is the step most often skipped and most often asked about in marking.

Complex roots are given properly, in the form p plus or minus qi, rather than the page refusing to answer. A negative discriminant is not an error; it means the parabola never crosses the x-axis, which is a perfectly ordinary situation and one that matters in physics and engineering as much as in algebra.

The vertex, the axis of symmetry and whether the parabola opens upwards or downwards are shown alongside, since those are usually the next things asked for. Where the roots are rational, the factorised form is given too.

Everything is worked out inside your browser. Nothing you enter is uploaded, logged or stored, which matters for the financial calculators in particular: the figures you put into them are nobody else's business.

• Real and complex roots, both handled properly
• Discriminant reported first, with what it means
• Vertex and axis of symmetry
• Factorised form where the roots are rational
• Exact surd form as well as decimals
• Full step-by-step working
• Runs in your browser

The quadratic equation solver is used by writers, developers, students, marketers and anyone else who needs the job done once without installing software. Common cases include:

• Algebra homework where the method is marked
• Checking an answer you worked out by hand
• Finding where a projectile lands
• Solving for break-even in a quadratic cost model
• Teaching the discriminant with worked examples