Frequently Asked Questions
Common questions about the free quadratic equation solver — how it works, real and complex roots, step-by-step working, the discriminant, the graph, and privacy.
How does the quadratic equation solver work?
Enter the coefficients a, b, and c from your equation (ax² + bx + c = 0) and the tool instantly calculates the roots using the quadratic formula, along with step-by-step working — no button refresh needed.
Is this quadratic solver free to use?
Yes, it's completely free with no sign-up, downloads, or limits. Solve as many equations as you need, as often as you like.
Does it show the steps?
Yes. The solver shows the full step-by-step solution using the quadratic formula, so you can follow exactly how the answer is reached — identifying the coefficients, calculating the discriminant, classifying the root type, and applying the formula to get each root. Not just the final result.
Can it solve equations with complex roots?
Yes. When the discriminant is negative, the solver returns the complex (imaginary) roots in a + bi form rather than just saying there is no real solution. The step-by-step working shows exactly how the imaginary parts are derived.
What is the discriminant and why does it matter?
The discriminant (Δ = b² − 4ac) tells you how many roots an equation has and what type they are. If Δ > 0, there are two distinct real roots. If Δ = 0, there is exactly one repeated real root. If Δ < 0, there are two complex roots. The tool calculates and displays the discriminant prominently so you always know what to expect before reading the roots.
Does it graph the equation?
Yes. The solver plots the parabola for your equation, marks the roots with dots on the x-axis (for real roots), and highlights the vertex. This makes it easy to visualise whether the parabola crosses the x-axis, just touches it, or floats entirely above or below it.
What if a is 0?
If a is 0 the equation is not quadratic — without an x² term it becomes a linear equation (bx + c = 0). The tool will display a clear error message rather than attempting to calculate an invalid result. Enter any non-zero value for a to use the quadratic solver.
Is my data stored anywhere?
No. Your inputs are processed directly in your browser and are never stored or sent to a server, keeping your work completely private. Close the tab and everything is gone.
Does it work on mobile devices?
Yes, the tool is fully responsive and works on smartphones, tablets, and desktops without any installation. The input fields, step-by-step working, and graph all adapt to the screen width.
How accurate are the results?
Calculations use precise floating-point math, giving accurate roots, discriminant values, and graph points, including for complex and fractional results. For near-zero discriminants the solver applies a small tolerance to correctly classify them as the zero case rather than reporting spurious tiny imaginary parts.