I'm reading about negative normal forms. My text talks about transforming H¬x to 'negative normal form' so it reads ¬Hx.
If the two sentences are interchangeable, then they mean the same thing. So, suppose that H stands for reads a lot, and that x refers to someone named John. Could one think of ¬Hx translating in to it is not the case that John reads a lot, and of H¬x translating in to it is the case that John does not read a lot. (Although, I suppose they could both translate into any one English sentence that expresses their shared meaning.)
More importantly, why would anyone bother writing H¬x?
The negation of $x$ in that expression is formally wrong - and in formal logic everything is super technical and formal.
"Negative normal form" refers to when the not operator is fully distributed. Consider $\neg (A\wedge B)$ vs $\neg A\vee \neg B$. See here for more details.