We introduce a simple and predictive model for determining the phase stability of ternary phospholipid-cholesterol mixtures. Assuming that competition between the liquid and gel order of the phospholipids is the main driving force behind lipid segregation, we derive a Gibbs free-energy of mixing, based on the thermodynamic properties of the lipids main transition. A numerical approach was devised that enable the fast and efficient determination of the ternary diagrams associated with our Gibbs free-energy. The computed phase coexistence diagram of DOPC/DPPC/cholesterol reproduces well known features for this system at 10°C, as well as its evolution with temperature.