The approximate method to treat the practical quantum anharmonic solids proposed by Hardy. Lacks and Shukla is reformulated with explicit physical meanings. It is shown that the quantum effect is important at low temperature, it at be treated in the harmonic framework; and the anharmonic effect is important at high temperature and tends to zero at low temperature, it can be treated by using a classical approximation. The alternative formulation is easier for various applications, and is applied to a Debye-Gruneisen aolid with the generalized Lennard-Jones intermolecular interaction. The expressions for the Debye temperature and Grunelsen parameter as a function of volume are analytically derived. The analytic equation of state is applied to predict the thermodynamic properties of solid xenon at normal pressure with the nearest-neighbour Lennard-Jones interaction, and is further applied to research the properties of solid xenon and krypton at high pressure by using an all-neighbour Lennard-Jones interaction. The theoretical results are in agreement with the experiments.