In this article, a simple but quite accurate model conforming to observations and solving the modified Poisson equation is utilized in order to compute the rotation curves as well as the radial acceleration relations of spiral galaxies being composed of several components: the central region of the bulge, the bulge, the disk, and dark matter. With this model, flat rotation curves of spiral galaxies are obtained, because the modified Poisson equation approximately meets the requirement of conservation of total energy in Newton's theory of gravity, wherefore the model contains the exact circular speeds of test particles which are caused by the dark matter component of the respective considered spiral galaxies. The computed rotation curves are fitted to the observed speeds in spiral galaxies taken from SPARC. It turns out, that the simple model in this article is able to explain the observed flat rotation curves as well as the increasing rotation curves at large distances from the center of spiral galaxies with a very good accuracy.