Solve the following equation:

$$
\sqrt{x+5}+\sqrt{2 x+8}=7 .
$$
Squaring both sides of the equation:

$$
2 \sqrt{2 x^{2}+18 x+40}=36-3 x
$$

Squaring again and rearranging:

$$
x^{2}-288 x+1136=0
$$

from which

$$
x_{1}=284, x_{2}=4 \text {. }
$$

(János Krátky, Budapest.)