We propose here a simple theory for polydisperse, branched polyethylene dissolved in ethylene based on a cubic equation, namely the Sako-Wu-Prausnitz-equation of state, in combination with the Lattice Cluster Theory in the incompressible version, which is predictive concerning the branching, while using continuous thermodynamics to account for polydispersity with respect to the molecular mass. The new theory considers polymers to follow the Schulz-Flory distribution and to adopt an average degree of branching. It does not require different parameters for different molar masses, polydispersities or degrees of branching and hence, the number and mass average molar mass as well as average branch content are sufficient We parameterize this theory for ethylene based on critical data and for polyethylene based on simple arguments and some experimental data of n-alkanes. The binary parameter describing the dispersion energy and its temperature dependence stemming from Lattice Cluster Theory is fit to experimental cloud point data from literature of one specific sample of polyethylene in ethylene. The theory is then used to predict the cloud point curves and critical properties of nine other polyethylene samples in ethylene. The fit and predicted cloud point curves show quantitatively correct temperature dependence. For high polydispersities, the concentration dependence is only qualitatively correct, which is most probably due to the oversimplified Schulz-Flory distribution. The influence of branching on cloud point pressures and critical pressures at constant temperature is predicted quantitatively correct. (C) 2016 Elsevier B.V. All rights reserved.