[Calculus] Putnam paper

My homework is to wright a paper over an equation of which i have chosen an old putnam problem, and what i was wondering was if yall could look over my paper and see if i made any mistakes or had otherwise just made it look sloppy.

This is the Paper

My fears may be that i wrote too much wording, messed up in recording the calculations, or described the actions i was taking in a wrong manner.

The project itself was to solve the equation and write a paper in a similar style as to how textbooks explain solving equations, basically teaching the reader how to solve the problem.