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Quadratic Equation Solver

Solve quadratic equations ax² + bx + c = 0 with the quadratic formula. Shows discriminant, roots, vertex, and step-by-step solutions.

Solve quadratic equations of the form ax² + bx + c = 0 using the quadratic formula. Get instant results with discriminant analysis, vertex coordinates, and detailed step-by-step solutions.

  1. Enter the coefficients a, b, and c for ax² + bx + c = 0
  2. The equation preview and solution update in real-time
  3. View the discriminant (Δ), roots, vertex, and axis of symmetry
  4. Follow the step-by-step solution to understand the process
  • Quadratic formula — Solves using x = (−b ± √Δ) / 2a
  • Discriminant analysis — Shows Δ value and what it means
  • Vertex & axis — Displays parabola vertex and axis of symmetry
  • Complex roots — Shows complex solutions when Δ < 0
  • Step-by-step — Detailed solution breakdown
What is the quadratic formula?
x = (−b ± √(b²−4ac)) / 2a — it gives the solutions to any quadratic equation ax² + bx + c = 0.
What is the discriminant?
The discriminant Δ = b²−4ac determines the nature of the roots: positive means 2 real roots, zero means 1 double root, negative means complex roots.
What is the vertex?
The vertex is the highest or lowest point of the parabola, located at (−b/2a, f(−b/2a)).
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Step-by-step Solution
Enter coefficients to solve
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ax² + bx + c = 0
Discriminant (Δ)
Vertex
Axis of Symmetry
Step-by-step Solution
Enter coefficients to solve
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Step-by-step Solution
Enter coefficients to solve
Enter coefficients a, b, c for ax² + bx + c = 0
Coefficient a must not be 0 (otherwise it's linear)
Δ > 0 — Two distinct real roots
Δ = 0 — One double root
Δ < 0 — No real roots (complex)
Want to learn more? Read documentation →
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