Answer
$t=\pm\dfrac{\sqrt{30}}{6}$
Work Step by Step
Since $x^2=a$ implies $x=\pm\sqrt{a}$ (the Square Root Principle), the solutions to the given equation, $
6t^2-5=0
,$ are
\begin{array}{l}\require{cancel}
6t^2=5
\\\\
t^2=\dfrac{5}{6}
\\\\
t=\pm\sqrt{\dfrac{5}{6}}
\\\\
t=\pm\sqrt{\dfrac{5}{6}\cdot\dfrac{6}{6}}
\\\\
t=\pm\sqrt{\dfrac{30}{36}}
\\\\
t=\pm\dfrac{\sqrt{30}}{\sqrt{36}}
\\\\
t=\pm\dfrac{\sqrt{30}}{\sqrt{(6)^2}}
\\\\
t=\pm\dfrac{\sqrt{30}}{6}
.\end{array}
