Equation Solver
Choose the equation type and enter the coefficients. The solver shows each step — isolating x for linear equations, or the discriminant and quadratic formula for quadratics — including complex roots when there are no real solutions.
- x₁
- 5
- x₂
- -2
- Vertex
- (1.5, -12.25)
Steps
- Discriminant D = b² − 4ac = (-3)² − 4(1)(-10) = 49
- x = (−b ± √D) ÷ 2a = (3 ± √49) ÷ 2
Worked example
Example: x² − 3x − 10 = 0
- a = 1, b = −3, c = −10
- D = (−3)² − 4(1)(−10) = 9 + 40 = 49
- x = (3 ± 7) ÷ 2
x = 5 or x = −2.
Formula
Linear: x = (c − b) ÷ a
Quadratic: x = (−b ± √(b² − 4ac)) ÷ 2a
The discriminant D = b² − 4ac tells you the number of real roots: two if D > 0, one if D = 0, none (two complex) if D < 0.
Frequently asked questions
How do I solve a two-step equation?
Undo addition/subtraction first, then multiplication/division. For 2x + 3 = 11: subtract 3 (2x = 8), then divide by 2 (x = 4).
What if a = 0 in a quadratic?
Then it's a linear equation bx + c = 0 and the solver treats it that way.
What are complex roots?
When D < 0, the roots involve i = √−1, like −1 ± 2i. The parabola doesn't cross the x-axis.
Last reviewed October 17, 2026 · Calculations run in your browser; nothing you enter is sent to a server.