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x²

Quadratic Equation Solver

Full solution of ax²+bx+c=0 with the discriminant and a graph.

1x² − 3x + 2 = 0
Discriminant: Δ = b² − 4ac = 1
Number of solutions: Two real solutions
x₁ = 2
x₂ = 1
Step-by-step solution
  1. Identify coefficients: a = 1, b = -3, c = 2
  2. Discriminant: Δ = b² − 4ac = -3² − 4 × 1 × 2 = 1
  3. Conclusion: Δ > 0 — two real solutions
  4. Substitute into the formula: x = (−b ± √Δ) / 2a = (−(-3) ± √1) / (2 × 1)
  5. Answer: x₁ = 2, x₂ = 1
Graph of the parabola
Examples

How to use it

  • Enter the coefficients a, b, c of the equation ax² + bx + c = 0.
  • The tool computes the discriminant Δ = b² − 4ac.
  • The sign of Δ determines the number of solutions: two, one, or no real solution.
  • The graph shows the parabola and its intersection points with the x-axis.

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✍️ Written by the MathsUK teamChecked against the National Curriculum and GCSE specifications