#### Answer

$x=\pm4$

#### Work Step by Step

Using the properties of equality, the given equation, $
3x^2-1=47
,$ is equivalent to
\begin{array}{l}\require{cancel}
3x^2=47+1
\\\\
3x^2=48
\\\\
x^2=\dfrac{48}{3}
\\\\
x^2=16
.\end{array}
Taking the square root of both sides, then the solutions of the given equation are
\begin{array}{l}\require{cancel}
x=\pm\sqrt{16}
\\\\
x=\pm\sqrt{(4)^2}
\\\\
x=\pm4
.\end{array}