a) To solve x² - 7x + 6 = 0, we need to factor the quadratic equation.

The equation can be factored as (x - 6)(x - 1) = 0

Setting each factor to zero gives us:

x - 6 = 0 or x - 1 = 0

So, x = 6 or x = 1

Therefore, the solutions to the equation x² - 7x + 6 = 0 are x = 6 and x = 1.

b) To solve x² - 4x - 21 = 0, we can use the quadratic formula:

x = [-(-4) ± √((-4)² - 4(1)(-21))] / 2(1)
x = [4 ± √(16 + 84)] / 2
x = [4 ± √100] / 2
x = [4 ± 10] / 2

So, x = (4 + 10) / 2 or x = (4 - 10) / 2

x = 14 / 2 or x = -6 / 2
x = 7 or x = -3

Therefore, the solutions to the equation x² - 4x - 21 = 0 are x = 7 and x = -3.