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Type in a, b, and c — Axiom shows every step, starting with the discriminant.
Rearrange the equation into ax² + bx + c = 0 and enter a, b, and c with their signs. Press Solve step-by-step to see the discriminant and real solutions; a must be nonzero.
The discriminant D = b² − 4ac determines the real-root case: positive gives two roots, zero gives a repeated root, and negative gives no real roots. The quadratic formula is x = (−b ± √D)/(2a). This solver uses that formula rather than a separate factoring mode, with rounded decimals for numerical roots.
Enter 1, −5, 6 for x² − 5x + 6 = 0. D = 25 − 24 = 1, so x = (5 ± 1)/2 gives 2 and 3. Substituting either value makes the equation zero.
For x² − 6x + 9 = 0, enter 1, −6, 9. D = 36 − 36 = 0, giving x = 6/2 = 3. The curve touches the x-axis at that root.
For x² + 1 = 0, enter 1, 0, 1. D = −4, so there are no real solutions. Complex roots exist, but this tool does not output them.
Move all terms to one side first. For x² = 5x − 6, enter the equivalent equation x² − 5x + 6 = 0, using 1, −5, and 6.
No. Removing x² makes the equation linear. Use the Linear Equation Solver for that case instead.
No. A negative discriminant produces a no-real-solutions message. It does not mean the equation has no solutions over the complex numbers.
If it factors cleanly, you can verify a result by hand: x² − 5x + 6 = (x − 2)(x − 3), so the roots are 2 and 3. This calculator does not factor the equation; it finds real roots with the quadratic formula.
No. The formula is the symbolic expression, while displayed decimal roots are approximations. A near-zero discriminant may be treated as zero within floating-point precision.
Plot the same coefficients in the graphing calculator to connect roots with x-intercepts. For first-degree equations use the linear solver, and read the quadratic equations lesson for the reasoning behind the formula. Related tools: Linear & Quadratic Graphing Calculator, Linear Equation Solver. Read the Quadratic Equations lesson or practice quadratic equations to build confidence without relying on a calculator.