The PC-SAFT equation of state is a very popular and promising model for fluids that employs a complicated pressure-explicit mathematical function (and can therefore not be solved analytically at a specified pressure and temperature, contrary to classical cubic equations). In this work, we demonstrate that in case of pure fluids, the PC-SAFT equation may exhibit up to five different volume-roots whereas cubic equations give at the most three volume-roots (and yet, only one or two volume roots have real significance). The consequence of this strongly atypical behaviour is the existence of two different fluid-fluid coexistence lines (the vapour pressure-curve and an additional liquid-liquid equilibrium curve) and two critical points for a same pure component, which is obviously physically inconsistent. In addition to n-alkanes, nearly sixty very common pure components (branched alkanes, cycloalkanes, aromatics, esters, gases, and so on) were tested out and without any exception, we can claim that all of them exhibit this undesired behaviour. In addition, such similar phenomena (i.e. existence of more than three volume-roots) may also arise with mixtures. From a computational point of view, most of the algorithms used for solving equations of state only search for three roots at the most and are thus likely to be inefficient when an equation of state gives more than three volume-roots. To overcome this limitation, a simple procedure allowing to identify all the possible volume-roots of an equation of state is proposed.