One of the main problems of celestial mechanics is how to determine the motions of three bodies caused by exertion of the forces of the mutual gravitational attraction. Under the influence of the gravitational forces, individual bodies orbit around a mutual centre of gravity. When analyzing their motions, it is necessary to determine the positions and velocities of the bodies at any moment in the past or future. When three bodies are concerned, this is impossible to solve completely. J. L. Lagrange proved that in special cases there is a completely analytical solution to the motions of three bodies when the third body is positioned in one of the five libration points in relation to the first two bodies. Those positions are called Lagrangian points. In this paper, I have shown the derivation of the position of those points.