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Using quadratic Formula , solve the following for x :

9x²- 3 ( a + b )x + ab

$9 x^{2} - 3 (a + b) x + a b = 0 ∴ x = \frac{- (- 3 (a + b)) \pm \sqrt{(- 3 (a + b))^{2} - 4 (9) (a b)}}{2 (9)} = \frac{3 (a + b) \pm \sqrt{9 (a + b)^{2} - 36 a b}}{18} = \frac{3 (a + b) \pm \sqrt{9 a^{2} + 9 b^{2} + 18 a b - 36 a b}}{18} = \frac{3 (a + b) \pm \sqrt{9 a^{2} + 9 b^{2} - 36 a b}}{18} = \frac{3 (a + b) \pm 3 (a - b)}{18} = \frac{(a + b) \pm (a - b)}{6} ∴ x = \frac{(a + b) + (a - b)}{6} o r x = \frac{(a + b) - (a - b)}{6} = \frac{a}{3} = \frac{b}{3} ∴ x = \frac{a}{3} o r x = \frac{b}{3}$

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