2(9a-6)^2=11(9a-6)+63

2(9a-6)^2-11(9a-6)-63 = 0
If you rewrite this using u = 9a-6, you just have

2u^2-11u-63 = 0
(2u+7)(u-9) = 0
u = -7/2 or u=9
That means

9a-6 = -7/2
18a-12 = -7
18a = 5
a = 5/18

9a-6 = 9
9a = 15
a = 5/3