Algebra Calculator

Solve linear equations and quadratic equations using standard algebraic formulas.

Linear: x = (c - b) / a; Quadratic: x = [-b +/- sqrt(b^2 - 4ac)] / 2a
Linear: 2x + 5 = 13 -> x = 4; Quadratic: x^2 - 5x + 6 = 0 -> x = 2 or x = 3

How do you solve a linear equation?

Linear equation format: ax + b = c. Isolate x: Subtract b from both sides -> ax = c - b. Divide by a -> x = (c - b) / a. Example: 3x + 5 = 14 -> 3x = 9 -> x = 3. Check: 3(3) + 5 = 14 ✓. Key principle: Whatever you do to one side, do to the other. Goal: Get x alone on one side.

What is the quadratic formula and when do I use it?

Quadratic formula: x = [-b +/- sqrt(b^2 - 4ac)] / 2a for ax^2 + bx + c = 0. Use when equation has x^2 term. Discriminant (b^2 - 4ac): Positive = 2 real solutions, Zero = 1 solution, Negative = no real solutions (complex). Example: x^2 - 5x + 6 = 0 -> a=1, b=-5, c=6 -> x = (5 +/- 1)/2 -> x = 3 or x = 2.

What does the discriminant tell you?

Discriminant = b^2 - 4ac determines solution types: Positive (e.g., 25): Two different real solutions. Zero: One repeated real solution (perfect square). Negative (e.g., -8): No real solutions, two complex solutions. Example: x^2 + 2x + 5 = 0 -> discriminant = 4 - 20 = -16 (negative) → no real solutions. Parabola doesn't cross x-axis.

How do you check your algebra answer?

Substitute solution back into original equation. Example: Solved 2x + 3 = 11, got x = 4. Check: 2(4) + 3 = 8 + 3 = 11 ✓. For quadratic: Both solutions should satisfy equation. If check fails, recalculate - you made an error. Always verify, especially on tests. Most algebra mistakes happen in arithmetic, not concept.