Answer
\[\left\{ { - 1,4} \right\}\]
Work Step by Step
\[\begin{gathered}
\left| {\begin{array}{*{20}{c}}
x&3 \\
x&x
\end{array}} \right| = 4 \hfill \\
{\text{Expand the determinant to obtain}} \hfill \\
\left( x \right)\left( x \right) - \left( x \right)\left( 3 \right) = 4 \hfill \\
{x^2} - 3x = 4 \hfill \\
{\text{Solve the equation}} \hfill \\
{x^2} - 3x - 4 = 0 \hfill \\
\left( {x - 4} \right)\left( {x + 1} \right) = 0 \hfill \\
{x_1} = 4,\,\,\,\,{x_2} = - 1 \hfill \\
{\text{The solution set is}} \hfill \\
\left\{ { - 1,4} \right\} \hfill \\
\end{gathered} \]
