Answer
$$\left\{ { - 4} \right\}$$
Work Step by Step
$$\eqalign{
& \left| {\matrix{
{ - 2} & 0 & 1 \cr
{ - 1} & 3 & x \cr
5 & { - 2} & 0 \cr
} } \right| = 3 \cr
& {\rm{Expand \,the \,determinant\, to\, obtain}} \cr
& - 2\left| {\matrix{
3 & x \cr
{ - 2} & 0 \cr
} } \right| - 0 + 1\left| {\matrix{
{ - 1} & 3 \cr
5 & { - 2} \cr
} } \right| = 3 \cr
& - 2\left( {0 + 2x} \right) + \left( {2 - 15} \right) = 3 \cr
& {\rm{Solve\, the\, equation}} \cr
& - 4x - 13 = 3 \cr
& - 4x = 16 \cr
& x = - 4 \cr
& {\rm{The\, solution\, set \,is}} \cr
& \left\{ { - 4} \right\} \cr} $$
