Deleting the original question and creating a new one seems like... cheating somehow?
It isn't cheating. But that's not the recommended course of action.
Check any thread by anyone who ever hit a post ban. They all say: "Try salvaging your posts by editing them into shape".
If you like badges notice there's a positive/negative question record that impacts your Curious/Inquisitive/Socratic badge awards.
In the above 2 scenarios deleting clearly counts against you. Depending on your rep and track-record this may range from having nearly no impact to significantly changing your participation.
- Take care if posting a new overhauled version of the question without deleting the old one, there's still a chance someone might consider both questions similar enough and vote for closure as a self-duplicate. (Which would count towards aggravating the 2 former points.)
The question got downvoted and my problem was left without a solution.
Edit it. That's enough for the downvoters to be able to reverse their vote. Some users might be following your question and tag watchers are also likely to not have read it yet, or revisit it if there's recent activity.
NOTE: In these cases it might be better to temporarily delete the question in order to calmly edit it - you can undelete it when you're done. (That way the post is kept out-of-view and temporarily protected from further downvotes and comments.)
Vote counts can auto-correct after edits. All things considered editing is still, probably, your best course of action.