I've got
$3\sqrt{x+4}-2\sqrt{x-11}+5\sqrt{x-8}=0$ and I have to evaluate $x$. I tried \begin{align} &&3\sqrt{x+4}-2\sqrt{x-11}+5\sqrt{x-8}&=&0 \\ &\Leftrightarrow& 3\sqrt{x+4}+5\sqrt{x-8}&=&2\sqrt{x-11} \\ &\Leftrightarrow& (3\sqrt{x+4}+5\sqrt{x-8})^2&=&4(x-11) \\&\Leftrightarrow& 9(x+4)+30(\sqrt{x+4}\sqrt{x-8})+25(x-8)&=&4(x-11)\\ &\Leftrightarrow& 9x+36+30(\sqrt{x^2-4x-32})+25x-200&=&4x-44\\ &\Leftrightarrow& \frac{5x+80}{30}&=&\sqrt{x^2-4x-32} \\ &\vdots&\end{align}
If I continue I don't get a proper solution for $x$, so I would like to know if the first steps are correct or if I should try something else?
Thanks a lot in advance