I don't know why it's there either. It certainly doesn't need to be there, and I would assume it's actually an error or at the very least unnecessary.

You can have both a’s, no a’s, or a single ‘a’ in either place. The differences in meaning are very slight.

The sentence has this form: "My enrollment was the result of (a) NOUN." ("a", "the", "some", "my".... are optional) You can insert any noun or noun clause and you will have a correct sentence. For example: "My enrollment was the result of a whim." "My enrollment was the result of the balloon that I saw in the sky above one year ago." "My enrollment was a result of my cat's wayward ways." "My enrollment was the result of chocolate." ...and so forth. Determiners like "what" or "that" often introduce noun clauses: "What you think influences what you do." "That you sing is fortunate." "The floor being dirty is the result of what the dog did." "My enrollment was the result of what I believed was a misspent youth." To that, you can add determiners and it will still be correct because determiners can be placed in front of nouns: "My enrollment was the result of a what I believed was a misspent youth." "My enrollment was the result of my what I believed was a misspent youth." "My enrollment was the result of the what I believed was a misspent youth." The last three are a bit awkward, but they make grammatical sense. If I were to eliminate an "a", it is the SECOND one that I would eliminate: "My enrollment was the result of a what I believe to have been misspent youth."

give the whole sentence and then it will be clear why there's "a" there