Answer
$-2,3$
Work Step by Step
The determinant of a $2 \times 2$ matrix can be computed by using the formula $det =ps-qr$
where $det =\begin{bmatrix}p & q \\r & s\end{bmatrix}$
After simplifying, this matrix yields: $0=(x+4)(x-5) - (-2)(7) $
We need to set the expression equal to $0$.
Thus, we have: $x^2-x-6=0$
or, $(x-3)(x+2)=0$
So, $x=-2,3$
