Solve ax² + bx + c = 0 with step-by-step solution
Built & maintained by Pappu Venkata Subbi Reddy, founder of Clacify
Clacify's Quadratic Solver finds the roots of any quadratic equation ax² + bx + c = 0 using the quadratic formula: x = (−b ± √(b² − 4ac)) ÷ 2a. It shows the discriminant (Δ = b² − 4ac), determines whether roots are real and distinct (Δ > 0), real and equal (Δ = 0), or complex conjugates (Δ < 0), and displays the step-by-step working. Covers standard, vertex, and factored forms.
The quadratic formula solves ax² + bx + c = 0: x = (−b ± √(b² − 4ac)) ÷ 2a. The ± gives two roots. The discriminant (b² − 4ac) determines root type: positive = two distinct real roots, zero = one repeated real root, negative = two complex (imaginary) roots.
Example: 2x² − 7x + 3 = 0. a=2, b=−7, c=3. Discriminant = (−7)² − 4(2)(3) = 49 − 24 = 25. √25 = 5. x = (7 ± 5) ÷ 4. Root 1: x = 12/4 = 3. Root 2: x = 2/4 = 0.5. Check: 2(9)−7(3)+3 = 18−21+3 = 0 ✓.