Answer
\[\left\{ { - \frac{1}{2},6} \right\}\]
Work Step by Step
\[\begin{gathered}
\left| {\begin{array}{*{20}{c}}
{2x}&x \\
{11}&x
\end{array}} \right| = 6 \hfill \\
{\text{Expand the determinant to obtain}} \hfill \\
\left( {2x} \right)\left( x \right) - \left( {11} \right)\left( x \right) = 6 \hfill \\
2{x^2} - 11x = 6 \hfill \\
{\text{Solve the equation}} \hfill \\
2{x^2} - 11x - 6 = 0 \hfill \\
\left( {2x - 12} \right)\left( {2x + 1} \right) = 0 \hfill \\
2\left( {x - 6} \right)\left( {2x + 1} \right) = 0 \hfill \\
{x_1} = 6,\,\,\,\,{x_2} = - \frac{1}{2} \hfill \\
{\text{The solution set is}} \hfill \\
\left\{ { - \frac{1}{2},6} \right\} \hfill \\
\end{gathered} \]
