Answer
The solution is $h=7$.
Work Step by Step
The given equation is
$\Rightarrow \sqrt{8h-7}=\sqrt{6h+7}$
Square each side of the equation.
$\Rightarrow (\sqrt{8h-7})^2=(\sqrt{6h+7})^2$
Simplify.
$\Rightarrow 8h-7=6h+7$
Add $7-6h$ to each side.
$\Rightarrow 8h-7+7-6h=6h+7+7-6h$
Simplify.
$\Rightarrow 2h=14$
Divide each side by $2$.
$\Rightarrow h=7$
Check $h=7$.
$\Rightarrow \sqrt{8h-7}=\sqrt{6h+7}$
$\Rightarrow \sqrt{8(7)-7}=\sqrt{6(7)+7}$
$\Rightarrow \sqrt{56-7}=\sqrt{42+7}$
$\Rightarrow \sqrt{49}=\sqrt{49}$
$\Rightarrow 7=7$
True.
Hence, the solution is $h=7$.
