Is there a way to solve the following equation for $v_n^2$? I am working through a problem and I feel like there should be a way to solve it, but I am not sure how to do it:
$$v_n^2-(1+\eta)=-i\omega_n+\frac{i\omega_n}{\gamma_sv_n^2}$$
$$v_n^4+v_n^2 (i\omega_n-1-\eta)-\frac{i\omega_n}{\gamma_s}=0$$