Is there any good to keep the your answers with $0$ votes or it's better to delete them?
I've answered some questions lately and some are left without a comment or anything. What's your experience with this issue?
An answer with $0$ votes does not hurt your reputation. If it is a good answer, it helps the site and someone may discover that it is a good answer and upvote it in the future.
If it is a good answer, leave it.
Unless I notice (or am notified of) serious problems with an answer of mine, I keep them around, regardless of the score. I see no reason to delete such answers, as there is no telling whether some future visitor may come across an answer and find them valuable. Heck, it's possible that users have already found these answers valuable, but haven't gained enough reputation to upvote them.
Yes, in my opinion, it's not even close -- you should leave up any answer without wrong mathematics.
I get the sense that upvotes don't work very well for answers (they work very well for questions). There is almost no correlation between the answers I write that I like very much and the answers I like that get upvotes.
Do I hear some frustration here? In one or two months, you will probably be pleasantly surprised when some of your old zero vote answers receive an upvote. Explanation: You probably answered quite a few questions from users not having enough reputation yet to upvote your answers. These users very rarely realize that they can accept your answer. What happens over time is that either these users gain enough reputation to upvote your answer, or else the taskforce to cleanup the unanswered queue will upvote your answer, because questions without an upvoted or accepted answer are treated as unanswered. Let me assure you that these people read your answer first, and only upvote it if it answers the question.