Example 12. Solve the equation

$$
\sqrt{2 x+5}+\sqrt{x-1}=8
$$
Solution. Domain of the equation: $x \geqslant 1$. Squaring both sides of the equation and performing transformations, we obtain the equation

$$
2 \sqrt{2 x^{2}+3 x-5}=60-3 x
$$

After squaring both sides of this equation, we get the equation

$$
4\left(2 x^{2}+3 x-5\right)=(60-3 x)^{2}
$$

which is a consequence of the original equation. The roots of this equation are: $x_{1}=10$ and $x_{2}=362$.

The number $x_{2}=362$ is an extraneous root of the original equation, as for it, the equation being squared $2 \sqrt{2 x^{2}+3 x-5}=60-3 x$ has parts of different signs.

The number $x_{1}=10$ belongs to the domain of the original equation and satisfies it; therefore, it is its only root.