This paper tackles the capacity optimization problem for Device-to-Device (D2D) coexisting with long term evolution (LTE) cellular system. We firstly derive and analyse the probability density functions of the Signal-to-Interference Ratio (SIR). We show that the capacities of both D2D and LTE are concave and convex respectively w.r.t the transmitted power ratio. To maximize the capacity sum of both systems, we propose to use the convex concave procedure (CCCP) to obtain the optimal transmitted power ratio and we show that the optimal solution leads to a fair solution to both systems. This study is very crucial for the resource allocation and management phase, and can be exploited to better enhance the overall Quality of Service (QoS) of both systems.