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Quadratic Equation Solver

For an equation ax^2 + bx + c = 0, the roots are x equals minus b plus or minus the square root of (b squared minus 4ac), all divided by 2a. The expression b squared minus 4ac is called the discriminant and tells you how many real roots exist before you finish the calculation. Th

Calculators

For an equation ax^2 + bx + c = 0, the roots are x equals minus b plus or minus the square root of (b squared minus 4ac), all divided by 2a. The expression b squared minus 4ac is called the discriminant and tells you how many real roots exist before you finish the calculation. Th

This free Quadratic Equation Solver from KX Toolkit is part of our all-in-one online toolkit. It runs entirely in your browser, so your data never leaves your device for client-side operations. 100% free, forever - no paywall, no credit card, no trial.

How to use the Quadratic Equation Solver

  1. Enter your inputs (date, amount, rate, etc.).
  2. Pick any optional settings (tax mode, country, unit).
  3. Read the result - most calculators update as you type.
  4. Copy the result, or screenshot the breakdown for your records.

What you can do with the Quadratic Equation Solver

  • Quick personal-finance maths before a major purchase.
  • Tax estimates for freelancers and small businesses.
  • Verify a number on an invoice or receipt.
  • Help kids with homework calculations.

Why use KX Toolkit's Quadratic Equation Solver

  • Browser-based: Works on Windows, macOS, Linux, iOS and Android - no install, no extension.
  • Privacy-first: Client-side tools never upload your data; server-side tools delete files right after processing.
  • Mobile-friendly: Full feature parity on phones and tablets - not a stripped-down view.
  • Fast: Optimised for instant feedback. No artificial waiting screens, no email-gated downloads.
  • One hub for everything: 300+ tools across SEO, text, image, PDF, code, color, calculators and more - skip switching between sites.

Tips for the best results

For currency-aware calculators (GST, tax), always confirm the rate matches the jurisdiction on your invoice - rates change yearly.

Related Calculators

If you find this tool useful, explore the full Calculators collection or browse our complete tool directory. KX Toolkit is built for marketers, developers, designers, students and anyone who needs a quick utility without signing up for yet another SaaS.

What is the quadratic formula?
For an equation ax^2 + bx + c = 0, the roots are x equals minus b plus or minus the square root of (b squared minus 4ac), all divided by 2a. The expression b squared minus 4ac is called the discriminant and tells you how many real roots exist before you finish the calculation. The calculator returns both roots in one step, including complex ones if needed.
What does the discriminant tell me?
If the discriminant is positive, you get two distinct real roots. If it is zero, the parabola touches the x-axis at one point and you get a single repeated root. If it is negative, there are no real roots; the roots are complex conjugates. Looking at the discriminant first is a quick way to know what kind of answer to expect.
What if a equals zero?
Then the equation is not quadratic; it is linear (bx + c = 0). The calculator detects this and either solves it as a linear equation or warns you to use the linear solver. Dividing by 2a in the quadratic formula would also break, which is why guarding for a equals zero is a standard first step in any robust solver.
How do I get complex roots in plain language?
When the discriminant is negative, the square root is imaginary. The calculator splits the answer into a real part (minus b over 2a) and an imaginary part (square root of the absolute value of the discriminant, divided by 2a, multiplied by i). The two roots come as a complex conjugate pair, meaning they have the same real part and opposite imaginary signs.
Where are quadratic equations used in real problems?
Projectile motion in physics is a quadratic in time. Profit-maximisation problems in economics often reduce to quadratics. Engineers use them to find resonant frequencies; finance uses them in option pricing. Anywhere a graph traces a parabola, a quadratic is in the math. Knowing the formula by heart is one of the most reused tools across STEM fields.
Can the solver handle decimal coefficients?
Yes. Enter a, b, and c as decimals or fractions. Internally the calculator uses floating-point arithmetic, which is precise enough for almost all practical work. For symbolic exact answers (such as keeping the square root of 2 in the result rather than 1.4142), you would need a computer algebra system, but for numeric work this calculator is more than sufficient.

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