The mathematical modeling of solar cells and panels is critical in many photovoltaic applications. However, the standard single-diode solar cell model, commonly selected to model these devices, is implicit and difficult to integrate into simulation software. Therefore, exact explicit solutions of this model, more suitable for computing purposes, have been proposed based on the Lambert W-function. This work introduces an explicit single-diode, easy-to-use six-parameter solar cell model. The proposed model is formulated with elementary functions. The model is developed and tested over seven photovoltaic technologies as an alternative to traditional approaches. Results of the extensive comparison of the three models (implicit, explicit Lambert W, and explicit six-parameter) show that the proposed approach is more accurate (14.81% relative improvement on average compared to the traditional methods), almost as fast as the Lambert W approach and much faster than the implicit approach. Due to its simplicity and accuracy, the proposed model will become an alternative in photovoltaic applications such as energy prediction and maximum power point tracking.