Em dash next to displayed equation

Punctuation such as periods, commas, and occasionally question marks are usually put after display equations (your a = b + c), because they are are a part of the sentence (or part thereof) that ends with the equation. By contrast, your dash belongs to what follows the equation and thus it logically belongs there, i.e., your Option 1.

That being said, I fail to imagine a situation where starting a parenthesis (of any kind) after an equation is a good idea. This only happens if you have to have a thought and grammar that spans an equation and a parenthesis. One of those usually is too much already; two almost certainly are. For example, in your sentence, I won’t know what you actually want to tell me until the very last word (holds). What I actually did when first reading it was to scan ahead after equation to find the missing verb and only afterwards did I look at the equation and the parenthesis. So, the sentence is not in the order in which your reader actually wants to read it – that’s bad. If your sentence is more complex, the reader probably has to read it several times to find out what is going on.

Instead write something like:

Hence the following equation holds:
                    a = b + c,
where c must be nonzero.