Standard Model research troubles

Ran into a bit of trouble whilst researching the Standard Model. The Standard Model is an understanding of how fundamental particles and forces interact, but it is based upon a set of mathematical formulas known as a Lagrangian. This makes it slightly more difficult to explain why some of the inconsistencies exist in the Standard Model because I would like to avoid mentioning the Lagrangian in my report. It is very complex with many mathematical terms which I can not understand, which defeats the objective of my report which is to convey basic understanding of the work at the Large Hadron Collider and its significance in fairly basic terms.