1) Since we have a radical equation, we'll need probably to verify if the solution is valid. In Radical equations, extraneous solutions happen a lot. So let's solve this:
[tex]\begin{gathered} \sqrt{2x-4}=\sqrt{3x-8} \\ (\sqrt{2x-4)}^2=(\sqrt{3x-8})^2 \\ 2x-4=3x-8 \\ 2x-4+4=3x-8+4 \\ 2x=3x-4 \\ 2x-3x=3x-4-3x \\ -x=-4 \\ x=4 \end{gathered}[/tex]2) Let's now verify if this solution is correct since we need to avoid extraneous solutions:
[tex]\begin{gathered} \sqrt{2x-4}=\sqrt{3x-8} \\ \sqrt{2(4)-4}=\sqrt{3(4)-8} \\ \sqrt{4}=\sqrt{4} \\ 2=2\:True! \end{gathered}[/tex]