$2.16 \sqrt{x+1}-\sqrt{9-x}=\sqrt{2 x-12}$.

$2.171+\sqrt{1+x \sqrt{x^{2}-24}}=x$.
2.16 Raising both sides of the equation to the square, we have

$$
(x+1)+(9-x)-2 \sqrt{(x+1)(9-x)}=2 x-12, \text{ or }
$$

$\sqrt{(x+1)(9-x)}=11-x$.

Raising to the square again, after transformations we get $x^{2}-15 x+56=0$, from which $x_{1}=7, x_{2}=8$.

By checking, we are convinced that both roots are valid.

Answer: $\quad x_{1}=7, x_{2}=8$.