Answer
The solution is $v=6$.
Work Step by Step
The given equation is
$\Rightarrow \sqrt{2v-5}=\sqrt{\frac{v}{3}+5}$
Square each side of the equation.
$\Rightarrow (\sqrt{2v-5})^2=(\sqrt{\frac{v}{3}+5})^2$
Simplify.
$\Rightarrow 2v-5=\frac{v}{3}+5$
Add $5-\frac{v}{3}$ to each side.
$\Rightarrow 2v-5+5-\frac{v}{3}=\frac{v}{3}+5+5-\frac{v}{3}$
Simplify.
$\Rightarrow \frac{6v-v}{3}=10$
$\Rightarrow \frac{5v}{3}=10$
Multiply each side by $\frac{3}{5}$.
$\Rightarrow \frac{3}{5}\times \frac{5v}{3}=\frac{3}{5}\times 10$
Simplify.
$\Rightarrow v=6$
Check $v=6$.
$\Rightarrow \sqrt{2v-5}=\sqrt{\frac{v}{3}+5}$
$\Rightarrow \sqrt{2(6)-5}=\sqrt{\frac{6}{3}+5}$
$\Rightarrow \sqrt{12-5}=\sqrt{2+5}$
$\Rightarrow \sqrt{7}=\sqrt{7}$
True.
Hence, the solution is $v=6$.
