It is not a problem that the question is shown as active, which just means that recent activity has occurred on it. As far as what the system considers unanswered, having any (not deleted) answer that is accepted or has a positive score (based on votes) is sufficient. No further action is needed here.
Questions about problems that have been solved should not be closed for that reason. Basically, closure is for questions that ask the same thing as another question (they can be closed as duplicates) or that do not belong on the site (they can be closed for one of the other reasons).
Posting your own answer and accepting it is the right thing for you to have done on this post. However, your answer should actually answer your question. You should edit your question again, to remove the solution from it, and edit your answer, adding your solution to it.
Such edits will substantially improve the usability of your question and answer to others. Right now, your answer actually qualifies to be flagged as not an answer... but that isn't the right way to fix this. Instead, your solution should be placed in it, rather than in your question.
Anyone with editing privileges can do this--and other users can suggest edits--so this could potentially be solved without any further action from you. Normally I would just do that edit myself, upon seeing your post. But since you've posted this question on meta asking what to do with your question, I figured I may as well post an answer here and let you (or someone else, if they get to it first) take care of it.
As far as the status of your question in the Stack Exchange system goes, though, nothing further needs to be done.