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HomemathQuadratic Equation Solver

Quadratic Equation Solver

Solve quadratic equations (ax² + bx + c = 0) and find real or complex roots using the quadratic formula.

Our free Quadratic Equation Solver lets you solve quadratic equations (ax² + bx + c = 0) and find real or complex roots using the quadratic formula. It is built for students, teachers, engineers, and professionals who need fast, reliable math results who need fast, reliable results without installing software or creating an account.

Quadratic Equation Solver runs entirely in your browser on CalculatorsPlus — enter your values, get instant results, and copy or share your output in one click. Your data never leaves your device; we do not store inputs on any server.

Use the quadratic equation solver to verify manual work, explore "what if" scenarios, and save time on repetitive calculations. For learning, try solving the problem by hand first, then check your answer here.

Results update in real time as you change inputs, so you can explore "what if" scenarios — adjust one variable at a time to see how it affects the outcome before committing to a purchase, plan, or decision.

This page includes step-by-step instructions, frequently asked questions, and practical tips below the calculator. Bookmark it for repeat use — many math tasks come up weekly during projects, studies, or financial planning.

Common Uses

  • ✓Homework verification and exam preparation
  • ✓Quick checks during work, shopping, or DIY projects
  • ✓Teaching demonstrations and classroom examples
  • ✓Engineering and spreadsheet formula validation

How to Use the Quadratic Equation Solver

  1. 1

    Enter coefficient a

    Input the coefficient of x² (must not be zero).

  2. 2

    Enter coefficient b

    Input the coefficient of x.

  3. 3

    Enter coefficient c

    Input the constant term.

  4. 4

    View solutions

    See both roots, the discriminant, and vertex of the parabola.

💡 Tips & Tricks

  • •If a = 0, the equation is linear (not quadratic) — use standard algebra instead.
  • •The vertex form y = a(x-h)² + k gives you the maximum or minimum point.
  • •Factoring is faster than the formula when the roots are integers.

Frequently Asked Questions

What is the quadratic formula?
x = (-b ± √(b² - 4ac)) / 2a. This formula finds the roots (solutions) of any quadratic equation in the form ax² + bx + c = 0.
What is the discriminant?
The discriminant is b² – 4ac. If positive: 2 real roots. If zero: 1 repeated root. If negative: 2 complex (imaginary) roots.
What is a quadratic equation used for?
Quadratics model projectile motion, area optimization, profit maximization, trajectory calculation, and many physics/engineering problems.
Can a quadratic have no real solutions?
Yes, when the discriminant (b² – 4ac) is negative, the parabola does not cross the x-axis and the solutions are complex numbers involving i (√-1).

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