Equation Solver

Equation Solver

Solve linear and quadratic equations, including repeated, complex, identity and no-solution cases.

UNDERSTAND THE ANSWER

How is this calculated?

When a is zero, the solver automatically handles the equation as linear. A negative discriminant produces a complex conjugate pair.

Quadratic formulax = (−b ± √(b² − 4ac)) ÷ 2a

A practical example

For x² − 5x + 6 = 0, the discriminant is 1 and the roots are 3 and 2.

Assumptions, interpretation and common mistakes

Calculation assumptions

  • Coefficients represent ax² + bx + c = 0.
  • Coefficients are finite decimal numbers.
  • Displayed roots are rounded to twelve significant digits.

How to interpret the result

  • A positive discriminant gives two real roots.
  • A zero discriminant gives one repeated real root.
  • A negative discriminant gives a complex conjugate pair.

Common mistakes to avoid

  • Forgetting to move every term to one side so the other side equals zero.
  • Entering the constant term with the wrong sign.
  • Assuming a zero leading coefficient still defines a quadratic equation.