Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$t=5$
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.