We present the classical Bondi accretion theory for the case of non-isothermal accretion processes onto a supermassive black hole (SMBH), including the effects of X-ray heating and the radiation force due to electron scattering and spectral lines. The radiation field is calculated by considering an optically thick, geometrically thin, standard accretion disc as the emitter of UV photons and a spherical central object as a source of X-ray emission. In our analysis, the UV emission from the accretion disc is assumed to have an angular dependence, and the X-ray radiation from the central object is assumed to be isotropic. This allows us to build streamlines in any angular direction. The influence of both types of radiation is evaluated for different flux fractions of the X-ray and UV emissions with and without the effects of spectral line driving. We find that the radiation emitted near the SMBH interacts with the infalling matter and modifies the accretion dynamics. In the presence of line driving, a transition takes place from pure type 1 and 2 to type 5 solutions, which takes place regardless of whether the UV emission dominates the X-ray emission. We computed the radiative factors at which this transition occurs, and discard type 5 solution from all our models. We also provide estimated values of the accretion radius and accretion rate in terms of the classical Bondi values. The results are useful for constructing proper initial conditions for time-dependent hydrodynamical simulations of accretion flows onto SMBHs at the centre of galaxies.