  The relativistic precession model (RPM) can be used to obtain a precise
measurement of the mass and spin of a black hole when the appropriate set of
quasi periodic oscillations is detected in the power-density spectrum of an
accreting black hole. However, in previous studies the solution of the RPM
equations could be obtained only through numerical methods at a price of an
intensive computational effort. Here we demonstrate that the RPM system of
equations can be solved analytically, drastically reducing the computational
load, now limited to the Monte-Carlo simulation necessary to estimate the
uncertainties. The analytical method not only provides an easy solution to the
RPM system when three oscillations are detected, but in all the cases where the
detection of two simultaneous oscillations is coupled with an independent mass
measurement. We also present a computationally inexpensive method to place
limits on the black hole mass and spin when only two oscillations are observed.
