Answer
$t=1$
Work Step by Step
Squaring both sides of the given equation, $
\sqrt{3t+4}=\sqrt{4t+3}
,$ results to
\begin{array}{l}\require{cancel}
\sqrt{3t+4}=\sqrt{4t+3}
\\\\
\left( \sqrt{3t+4} \right)^2=\left( \sqrt{4t+3} \right)^2
\\\\
3t+4=4t+3
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
3t+4=4t+3
\\\\
3t-4t=3-4
\\\\
-t=-1
\\\\
t=1
.\end{array}
Upon checking, $
t=1
$ satisfies the original equation.