Example 16. Solve the equation

$$
\frac{3 x-2}{\sqrt{2 x-1}}=\sqrt{(2 x-1)^{3}}
$$
Solution. Solving the inequality $2 x-1>0$, we find the domain of the equation: $x>1 / 2$.

Multiplying both sides of the original equation by $\sqrt{2 x-1}$ and simplifying it, we obtain the equation

$$
4 x^{2}-7 x+3=0
$$

which is a consequence of the original equation. Its roots are: $x_{1}=1$ and $x_{2}=3 / 4$.

Both roots belong to the domain of the original equation. By substitution, we verify that both these roots are also roots of the original equation.