Quadratic Equation Examples
Worked examples for solving quadratic equations by factoring and by using the quadratic formula.
How to use the quadratic examples calculator
Use these examples to compare factoring and the quadratic formula for common high-school algebra problems.
- Try factoring if the trinomial has simple integer factors.
- Use the quadratic formula when factoring is not obvious.
- Check each root in the original equation.
Formula or method
x = (-b +/- sqrt(b^2 - 4ac)) / (2a).
Worked examples
Solve by factoring
Problem: x^2 - 5x + 6 = 0
Solution: (x - 2)(x - 3) = 0, so x = 2 or x = 3.
Use the quadratic formula
Problem: 2x^2 + x - 3 = 0
Solution: Discriminant is 25, so x = 1 or x = -3/2.