x^2 - 9x + 9 = 0 is not factorable, so we must use Quadratic Formula or complete the square. Since b is not even, completing the square is not that simple, involving fractions and all. So use Quadratic Formula.
x = [-b ± ?(b^2 - 4ac)]/(2a) = {-(-9) ± ?[(-9)^2 - 4(1)(9)]}/(2•1) = [9 ± ?(81 - 36)]/2 = [9 ± ?45]/2 = [9 ± 3?5]/2