Cant get my head around this...

It's probably something simple that I'm missing, but anyway...

sqrt(u - 3) = u - 5

the answer is supposedly u = 7
however, it's important to know why, so... well, why?

sqrt(u - 3) = u - 5
u - 3 = u^2 -10u + 25
0 = u^2 - 11u + 28
0 = (u -4)(u - 7)
u = 4 and u = 7

Plug them em into the original equation to check for extraneous roots.  With u = 4 you get 1 = -1, so you can throw that one out.  With u = 7 you get 2 = 2.  So u = 7.