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Solve the equation, 9x² - 9(a+b)x + (2a²+ 5ab+ 2b²) = 0

$9 x^{2} - 9 (a + b) x + (2 a^{2} + 5 a b + 2 b^{2}) = 0 \Rightarrow 9 x^{2} - 3 {(2 a + b) + (a + 2 b)} x + (2 a^{2} + 4 a b + a b + 2 b^{2}) = 0 \Rightarrow 9 x^{2} - 3 {(2 a + b) + (a + 2 b)} x + {2 a (a + 2 b) + b (a + 2 b)} = 0 \Rightarrow 9 x^{2} - 3 {(2 a + b) + (a + 2 b)} x + (2 a + b) (a + 2 b) = 0 \Rightarrow 9 x^{2} - 3 (2 a + b) x - 3 (a + 2 b) x + (2 a + b) (a + 2 b) = 0 \Rightarrow 3 x {3 x - (2 a + b) x} - (a + 2 b) {3 x - (2 a + b)} = 0 \Rightarrow {3 x - (a + 2 b)} {3 x - (2 a + b)} = 0 \Rightarrow 3 x - (a + 2 b) = 0 or 3 x - (2 a + b) = 0 \Rightarrow 3 x = a + 2 b or 3 x = 2 a + b \Rightarrow x = \frac{a + 2 b}{3} or x = \frac{2 a + b}{3}$

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