The equations for the magnon pairing theory of high-temperature copper-oxide-based superconductors are solved and used to calculate several properties, leading to results for specific heat and critical magnetic fields consistent with experimental results. In addition, the theory suggests an explanation of why there are two sets of transition temperatures (T(c) approximately 90 K and T(c) approximately 55 K) for the Y(1)Ba(2)Cu(3)O(6+x) class of superconductors. It also provides an explanation of why La(2-x)Sr(x)CuO(4) is a superconductor for only a small range of x (and suggests an experiment to independently test the theory). These results provide support for the magnon pairing theory of high-temperature superconductors. On the basis of the theory, some suggestions are made for improving these materials.