We derive the equations which determine the free energy, and other thermodynamic and structural properties, including the high-frequency dielectric constant, of a dipolar-quadrupolar polarizable liquid at the second level of renormalized perturbation theory (2-RPT). Our treatment is non-graphical and is based on simple arguments from electrostatics. The significance of the various parameters which enter the renormalized theory is discussed. Our results provide the starting point for calculations of the effects of many-body induction forces in molecular liquids.