Answer
$x=0$ or, $x=-9$
Work Step by Step
The determinant for a 3 by 3 matrix can be computed as:
$Determinant (D)= \begin{vmatrix} a & b & c \\
d & e & f \\
g & h & i \\ \end{vmatrix}=a(ei-fh)-b(di-fg)+c(dh-eg)$
We have:
$D= \begin{vmatrix}
x & 2 & 3 \\
1 & x & 0 \\
6 & 1 & -2 \\ \end{vmatrix}
$
Therefore, $D=x (-2x-0)-2(-2-0)+3(1-6x) \\=-2x^2+4+3-18x \\=-2x^2-18x+7$
Since, $det=7$
So, $-2x^2-18x=0 \implies -2x(x+9)=0$
$\implies x=0$ or, $x=-9$
