Answer
$t=5$
Work Step by Step
Squaring both sides of the given equation, $
\sqrt{2t-7}=\sqrt{3t-12}
,$ results to
\begin{array}{l}\require{cancel}
\sqrt{2t-7}=\sqrt{3t-12}
\\\\
\left( \sqrt{2t-7} \right)^2=\left( \sqrt{3t-12} \right)^2
\\\\
2t-7=3t-12
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
2t-7=3t-12
\\\\
2t-3t=-12+7
\\\\
-t=-5
\\\\
t=5
.\end{array}
Upon checking, $
t=5
$ satisfies the original equation.