Quadratic Formula Calculator
Solve Quadratic Formula step by step — enter coefficients or expressions to get roots, factors, or simplified forms with detailed algebraic working.
Formula
x = (-b ± √(b² - 4ac)) / 2a
Finds the x-intercepts of a quadratic function.
Worked Examples
Example 1: Standard Case
Problem:x² - 5x + 6 = 0
Solution:a=1, b=-5, c=6. Discriminant = 25 - 24 = 1. Roots = (5 ± 1)/2.
Result:x = 3, x = 2
Example 2: Complex Roots
Problem:x² + x + 1 = 0
Solution:a=1, b=1, c=1. Discriminant = 1 - 4 = -3.
Result:x = -0.5 ± 0.866i
Frequently Asked Questions
What is the quadratic formula?
x = (-b ± √(b² - 4ac)) / 2a. It calculates the roots (solutions) of a quadratic equation ax² + bx + c = 0.
Can I solve quadratics without this formula?
Yes. Methods include Factoring (if integers work), Completing the Square, or Graphing. The formula is reliable because it works for ALL quadratics.
What is the Standard Form of a quadratic?
y = ax² + bx + c. The graph is a parabola opening up (if a > 0) or down (if a < 0).