Global Navigation Satellite System Reflectometry (GNSS-R) can be successfully used to obtain information about the composition or the properties of ground surfaces, by analyzing GPS signals reflected by the ground. The received power of these signals is proportional to the moduli of the perpendicular and parallel polarization Fresnel coefficients, which in turn depend on the incidence angle and the ground's permittivity, a parameter related to the ground surface's physical properties. The goal is then to obtain the value of permittivity from the known value of the angle of incidence and the values of the Fresnel reflection coefficients, as measured by an automatic GNSS-R system. In general, the permittivity is a complex number: in some cases (e.g. for non-dispersive soils), its imaginary part can be neglected, and the permittivity can be assumed to be a real number. In this case, it is possible to solve the Fresnel reflection coefficients explicitly in terms of the permittivity. The corresponding solution formulas can then be used also to verify the validity of other empirical methods of determination of the permittivity. In this work, we present these formulas, and present a set of their verification, against know values of the permittivity obtained by independent measurements.