Answer
$\{-1,4\}$
Work Step by Step
We find the determinant of the given matrix as follows:
$\begin{vmatrix} x & 3 \\ x & x \\ \end{vmatrix}=x(x)-3(x)=x^2-3x$
Substitute the expression of the determinant in the given equation:
$x^2-3x=4$
Solve for $x$:
$x^2-3x-4=0$
$(x-4) (x+1)=0$
$x-4=0$ or $x+1=0$
$x=4$ or $x=-1$
The solution set of the given equation is:
$\{-1,4\}$
