We represent the superconducting ceramic compounds by the single band extended Hubbard model. We solve this model for the simultaneous presence of antiferromagnetism and the d-wave superconductivity in the Hartree-Fock (H-F) and in the coherent potential (CP) approximation, which is applied to the on-site Coulomb repulsion U. The hopping interaction used in addition to the Coulomb repulsion causes rapid expansion of the band at carrier concentrations departing from unity. This expansion shifts the d-wave superconductivity away from the half filled point reducing its occupation range approximately to the experimental range in the YBaCuO compound. The CP approximation used for the Coulomb repulsion is justified by the large ratio of Coulomb repulsion to the effective width of perturbed density of states being reduced by the hopping interaction. Fast disappearance of antiferromagnetism observed experimentally is supported by the relatively large value of the total width of unperturbed density of states. It is shown that our model is capable of describing the electron doped compounds as well.

23 pages, 13 figures