We investigate physical conditions under which nuclear matter may cross to quarkmatter using several equations of state for both phases. We calculate the combinede quation of state using the nuclear matter equation of state for low-density regionand the quark matter equation of state for the high-density region using Maxwellconstruction. Then we use it to calculate properties of non-rotating compact stars with quark cores and hadronic surface. We focus primarily on the maximum mass of a non-rotating star and on the moment of inertia of quark core for different com-binations of selected equations of state. This work is the starting point for futureinvestigation of rotating neutron stars with quark cores.