The quantum capacitance model is applied to obtain an exact solution for the space-resolved carrier density in a multigated doped graphene sheet at zero temperature, with quantum correction arising from the finite electron capacity of the graphene itself taken into account. The exact solution is demonstrated to be equivalent to the self-consistent Poisson-Dirac iteration method by showing an illustrative example, where multiple gates with irregular shapes and a nonuniform dopant concentration are considered. The solution therefore provides a fast and accurate way to compute spatially varying carrier density, on-site electric potential energy, as well as quantum capacitance for bulk graphene, allowing for any kind of gating geometry with any number of gates and any types of intrinsic doping. DOI: 10.1103/PhysRevB.87.125427