Quadratic Equation Solver

Solve quadratic equations using the quadratic formula, factoring, or completing the square. Get step-by-step solutions instantly.

Quadratic equations take the form ax² + bx + c = 0 and are essential in algebra, physics, and engineering. Our solver determines the best method to use, whether that is factoring, the quadratic formula, or completing the square, and walks you through every step. You will see the discriminant, the roots, and a clear explanation of whether the solutions are real or complex.

How It Works

Enter your equation or expression into the solver above and click "Solve." Our system first attempts a deterministic verification using a symbolic math engine for guaranteed accuracy. If verified, you will see a Verified badge next to the answer.

Example Problem

x² - 5x + 6 = 0

Step-by-Step Solution

  1. Identify a = 1, b = -5, c = 6
  2. Factor: find two numbers that multiply to 6 and add to -5: -2 and -3
  3. Write as: (x - 2)(x - 3) = 0
  4. Set each factor to zero: x = 2 or x = 3
Final Answer: x = 2 or x = 3

Frequently Asked Questions

What is the quadratic formula?
The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a). It works for any quadratic equation ax² + bx + c = 0.
How do you know if a quadratic has real solutions?
Calculate the discriminant b² - 4ac. If it is positive, there are two real solutions. If zero, one real solution. If negative, two complex solutions.
When should I use factoring vs the quadratic formula?
Use factoring when the equation has nice integer roots. Use the quadratic formula when factoring is not straightforward or when dealing with decimals or complex numbers.

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