Answer
$x=4$
Work Step by Step
$\sqrt{2x-1}=\sqrt{3x-5}$
$(\sqrt{2x-1})^{2}=(\sqrt{3x-5})^{2}$
$2x-1=3x-5$
$-1+5=3x-2x$
$x=4$
We need to confirm that $x=4$ works in the original equation:
Left side=$\sqrt{2(4)-1}=\sqrt{8-1}=\sqrt{7}$
Right side=$\sqrt{3(4)-5}=\sqrt{12-5}=\sqrt{7}$
Both sides agree, so the solutions works.