One root of the equation $\left|\begin{array}{ccc}3 x-8 & 3 & 3 \\ 3 & 3 x-8 & 3 \\ 3 & 3 & 3 x-8\end{array}\right|=0$ is:

$\frac{2}{3}$

The correct answer is Option (2) → $\frac{2}{3}$

$\left|\begin{array}{ccc}3 x-8 & 3 & 3 \\ 3 & 3 x-8 & 3 \\ 3 & 3 & 3 x-8\end{array}\right|=(3x-8)((3x-8)^2-9)-3(3(3x-8)-9)+3(9-3(3x-8))$

$⇒(3x-8)^3-9(3x-8)-9(3x-8)+27+27-9(3x-8)=0$

$⇒(3x-8)^3-27(3x-8)+54=0$

$⇒9x^3+512-72x(3x-8)-81x+216+54=0$

$⇒9x^3-216x^2+495x-242=0$

$∴x=\frac{2}{3}$