Solution by Factoring

1. Factor the quadratic equation:
   We need to find two numbers that multiply to 6 and add up to -5.
   These numbers are -2 and -3.
   So, x² - 5x + 6 = (x - 2)(x - 3)
2. Set each factor equal to zero:
   x - 2 = 0 or x - 3 = 0
3. Solve for x:
   x = 2 or x = 3

Solution using the Quadratic Formula

The quadratic formula is: x = [-b ± √(b² - 4ac)] / (2a)

1. Identify a, b, and c:
   For x² - 5x + 6 = 0:
   a = 1, b = -5, c = 6
2. Plug the values into the quadratic formula:
   x = [5 ± √((-5)² - 4 * 1 * 6)] / (2 * 1)
   x = [5 ± √(25 - 24)] / 2
   x = [5 ± √1] / 2
   x = [5 ± 1] / 2
3. Solve for x:
   x = (5 + 1) / 2 = 6 / 2 = 3
   or
   x = (5 - 1) / 2 = 4 / 2 = 2