Question 146734
x - Sqrt[-2 x + 21] = 9
Sqrt[-2 x + 21] = x - 9
-2 x + 21 = x^2 - 18 x + 81
0 = x^2 - 16 x + 60
0 = (x-6)(x-10)

gives x=6 or x=10,

but x=6 makes 6 - Sqrt[9]=3 which is not= 9. We therefore exclude this solution.

Leaving x=10 as the solution.