How did Homer Simpson work out the mass of the Higgs?

The extract below, which is from my book “The Simpsons and Their Mathematical Secrets”, explains how Homer Simpsons worked out the mass of the Higgs boson in the episode “The Wizard of Evergreen Terrace”.
The book does not contain the calculations required to derive the mass, but Megan Schmidt has kindly shown her workings, which are at the bottom of the page. (BTW Megan has a mathematics blog called MathyBeagle.)

Higgs Simpsons

Higgs workings