The present paper is concerned with the Tricomi-equation \[ \etasi_{hetaheta}+si_{\eta\eta}=0 \] This differential equation of mixed type is transformed in a formal-hyperbolic equation in the complex plane. The solutions of this equation are calculated by an integral operator. For this we consider a transformation for simplifying the differential equation. The kernel of this transformation can be represented in closed form. The integral operator also provides a way for studying some properties of the solutions. This equation can be solved as well for the subsonic and supersonic zone as for their transonic line $\eta=0$ which corresponds to the sound speed. Some particular solutions of the Tricomi-equation which are already known are special cases of this solution.