jmc

First, we start by squaring both sides of the equation $$\begin{array}{rl}(\sqrt{3x-5}{)}^2& =(2{)}^2\\ \Rightarrow 3x-5& =4\\ \Rightarrow 3x& =9\\ \Rightarrow x& =\boxed{3}.\end{array}$$Testing, we find that this value of $x$ does indeed satisfy the equation.