Resonance frequency of an LC oscillations circuit is stated as 

${\omega }_0=\frac{1}{\sqrt{LC}}$, here, $L \mathrm{and} C$ represents inductance and capacitance of circuit.

Now, when inductance and capacitance changes, i.e., $L^{\text{'}}=2L$ and $C^{\text{'}}=8C$

Then, resonant frequency is $\omega =\frac{1}{\sqrt{2L\times 8C}}=\frac{1}{4\sqrt{LC}}$

$\Rightarrow \omega =\frac{{\omega }_0}{4}$

Thus, the value of $x=\frac{1}{4}$.