This work presents an automatic and robust methodology for calculating phase equilibria with any equation of state (EOS). Its major advantage is applicability to the recent sophisticated thermodynamic approaches that exhibit multiple roots and which can challenge other methods. The proposed approach is based on the second-order geometrical approximation and the critical points as initial estimations. Its applications are illustrated by calculating phase equilibria in pure compounds by PC-SAFT, SAFT-VR, and the Johnson-Zollweg-Gubbins EOS along with the IAPWS formulation for water. The preliminary implementation to mixtures is discussed as well. Because this methodology requires determination of critical point coordinates, the relevant simple correlation and the Wolfram Mathematica code are provided.