For a resonant circuit,

$\dfrac{X_L}{R^2+X_L ^2}-\dfrac{1}{X_C} =0 \Rightarrow X_L.X_C =R^2 +X_L^2\\ \therefore \omega L.\dfrac{1}{\omega C}=R^2+\omega ^2 L^2 \Rightarrow \omega ^2 = \dfrac{1}{L^2}\left ( \frac{L}{C}-R^2 \right )\\ \therefore \omega =\sqrt{\dfrac{1}{LC}-\dfrac{R_2}{L^2}}\Rightarrow F_0=\frac{1}{2\pi}\sqrt{\frac{1}{LC}-\dfrac{R^2}{L^2}}$