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9x²-9(a+b)x +(2a² +5ab +2b²)=0

A = 9, B = -9(a+b), C = (2a² +5ab +2b²)

Solution of the above quadratic equation,

x = {-B±(B²-4AC)}/2A

={9(a+b)±(81(a+b)²-4x9x(2a² +5ab +2b²))}/18

= {9(a+b)±(81a² + 162ab + 81b² - 72a² - 180ab -72b²))}/18

= {9(a+b)±(9a² - 18ab + 9b²)}/18

= {9(a+b)±(9(a-b)²)}/18

= {9(a+b)±(3(a-b))}/18

Hence the solution is,

x = (2a+b)/3 and (a+2b)/3

Regards,

Team,

TopperLearning.