At parallel resonance

$I_C=I_L \sin \emptyset \\ \dfrac{V}{X_c}=\dfrac{V}{Z_L}\times \dfrac{X_L}{Z_L} \\ \dfrac{1}{X_c}=\dfrac{X_L}{Z^2_L} \\ Z_L^2=X_LX_C \\ Z_L^2=\dfrac{L}{C} \\ R^2+(2 \pi f_rL)^2=\dfrac{L}{C} \\ (2 \pi f_rL)^2=\dfrac{L}{C}-R^2 \\ f_r=\dfrac{1}{2 \pi f_r L} \sqrt{\dfrac{L}{C}-R^2} \\ f_r=\dfrac{1}{2 \pi f_r L} \sqrt{\dfrac{1}{LC}-\dfrac{R^2}{L^2}}$