$\displaystyle \sqrt{x-5} -\sqrt{x-8} =3$

This eventually works out to an $\displaystyle (A+B)^2$ = $\displaystyle A^2 + 2AB +B^2$ thing on the right side so that-

$\displaystyle x-8 + 2(\sqrt{x-8}+3) +3^2$

$\displaystyle \sqrt{x-5}$ = x-5 so that

x-5= x-8 + $\displaystyle 2(\sqrt{x-8}+3) +9$

Combining like terms: -8+9 = 1; and then I subtract 1 and x from both sides to get just a -6 on the left side.

After calculating all this out I came up with 9, but 9 doesn't work. The book says that the answer is 0 with a slash through it. Does that mean no solution because 9 is the only answer and doesn't check? I also checked it with zero and came up with

$\displaystyle -5 +2i\sqrt{2}=3$ That can't be right... right?

I thinkthismay be the problem: I'm thinking that my error may be in $\displaystyle 2(\sqrt{x-8}+3)$ Does that come out to

$\displaystyle 6\sqrt{x-8}$ which when squared =

$\displaystyle 36(x-8)$ which =$\displaystyle 36x-288$

Meanwhile on the left side I have 36, derived from $\displaystyle -6^2$ so that-

$\displaystyle 36=-288 +36x$: Add 288 to both sides to get $\displaystyle 324=36x$

324 divided by 36x= $\displaystyle 9$

I realized I've skipped over some steps for the sake of brevity, so if some clarity is needed I'm happy to provide. Any and all help is greatly appreciated. Thanks.