The solver uses the quadratic formula x = (−b ± √(b² − 4ac)) ÷ 2a. The discriminant b² − 4ac tells you whether there are two real roots, one repeated root, or two complex roots. Enter a, b and c to find the roots of ax² + bx + c = 0, with full working.
What does this tool do?
Solves ax² + bx + c = 0 completely: both roots, the discriminant, factorised form and vertex — with each step shown for homework. Handles real and complex roots.
The Quadratic Equation Solver also serves as a learning aid: watching results change as you drag inputs builds intuition for how the underlying formula behaves — which input moves the answer most, where the diminishing returns start, and what “good” looks like in real numbers rather than abstractions.
Using it is simple: the inputs are “a”, “b” and “c”. Results update live as you work — there is no waiting and nothing to submit.
How do I use this tool?
Enter your figures below — every result updates the instant you type, so comparing scenarios is just a matter of changing a number and watching the answer move.
- Enter your values in “a”, “b”, “c”.
- Results update instantly as you type — no button to press.
How does it work?
x = (−b ± √(b²−4ac)) / 2a. The discriminant D = b²−4ac decides: D>0 two real roots, D=0 one repeated root, D<0 two complex roots. The solver shows D, applies the formula, and simplifies.
The formula used is the standard one taught and published for this calculation — the tool does not invent methods. Where conventions differ (rounding, day-count, tax treatment), the page follows the common Pakistani practice and says so, so the result matches what local institutions expect.
Use cases in Pakistan
Quadratics are core BISE matric/inter maths (and MDCAT/ECAT-adjacent algebra). Beyond exams: projectile motion in physics, profit maximisation in business maths, and engineering calculations all reduce to quadratics.
Families use it for household budgeting and school-fee planning; small businesses for pricing and payroll math; students for everything from BISE numericals to CSS preparation. Wherever the same calculation is repeated monthly — bills, salaries, savings targets — this page replaces the phone-calculator ritual.
Limitations
It solves exactly what you enter — mistyped coefficients give confidently wrong roots. Word problems need translating to standard form first; the tool does not parse English into equations.
Assumptions are stated on the page — read them before trusting the headline number for money, health or legal decisions. A calculator amplifies the quality of its inputs: careful numbers in, trustworthy numbers out.
Frequently asked questions
What is the quadratic formula?
x = (−b ± √(b²−4ac))/2a for ax²+bx+c=0. Enter a, b, c above. For figures that go into applications or documents, double-check the inputs against the source — the math is exact, but only for the numbers you enter. Try varying one input at a time to see which assumption drives the result; that sensitivity check is often more valuable than the headline number.
What does the discriminant tell me?
b²−4ac: positive → two real roots; zero → one repeated root; negative → two complex roots. Try varying one input at a time to see which assumption drives the result; that sensitivity check is often more valuable than the headline number. Save or screenshot the result with its inputs when the figure matters later — reconstructing “what did I enter?” is harder than it sounds.
Can it show steps?
Yes — the discriminant, substitution and simplification are all displayed for homework checking. Save or screenshot the result with its inputs when the figure matters later — reconstructing “what did I enter?” is harder than it sounds. For figures that go into applications or documents, double-check the inputs against the source — the math is exact, but only for the numbers you enter.
What if a = 0?
Then it is not quadratic — it becomes linear (bx + c = 0), and the tool says so. For figures that go into applications or documents, double-check the inputs against the source — the math is exact, but only for the numbers you enter. Try varying one input at a time to see which assumption drives the result; that sensitivity check is often more valuable than the headline number.
Is my data uploaded or stored?
No. This tool runs entirely in your browser — what you type or paste never leaves your device, is never sent to a server, and is never stored. Closing the tab removes all trace. Try varying one input at a time to see which assumption drives the result; that sensitivity check is often more valuable than the headline number.
Is it really free? Do I need an account?
Yes, free, and no account needed. Open the page and use it — no sign-up, no trial, no watermark on results. Save or screenshot the result with its inputs when the figure matters later — reconstructing “what did I enter?” is harder than it sounds. For figures that go into applications or documents, double-check the inputs against the source — the math is exact, but only for the numbers you enter.
Updated October 2026 · Built and tested by Sharjeel Tahir · How our tools are tested