The Wannier equation can be generalized by including the presence of many electrons and holes in the excited system. One can start from the general theory of either optical excitations or light emission in semiconductors that can be systematically described using the semiconductor Bloch equations (SBE) or the semiconductor luminescence equations (SLE), respectively. The homogeneous parts of these equations produce the Wannier equation at the low-density limit. Therefore, the homogeneous parts of the SBE and SLE provide a physically meaningful way to identify excitons at arbitrary excitation levels. The resulting generalized Wannier equation is