Completely messed up an answer to a question, what do I do?

Question

I answered this question:

How to find the solutions $x$ of $ 2\sin{11^{\circ}}\sin{71^{\circ}}\sin{(x^{\circ}+30^{\circ})}=\sin{2013^{\circ}}\sin{210^{\circ}}$

but as you see, I completely misunderstood what OP was asking. I thought he meant he solved it in Wolfram by typing in the whole problem and it gave him the answer, where as (it seems) when he says he "can't use Wolfram", he means he can't use any kind of calculator and therefore he can't just type in $\arcsin (blah)$ into the calculator and solve it. So my answer is therefore apparently wrong and I got a down vote because of it.

I was just wandering what to do now. Should I delete it? Or should I leave it so other people can see my mistake and maybe put an edit on it saying what I thought the question was asking (I already have put a comment)?

Is there anything "protecting" me from downvotes or something because of the way OP didn't word the question properly?

I would like some feedback on this just so I understand how the site works a little better and so I can improve my answers. Thanks.

Answer 1

Should I delete it? Or should I leave it so other people can see my mistake and maybe put an edit on it saying what I thought the question was asking?

That is up to you entirely.

When I find out I totally misunderstood a question, I generally delete my wrong answer. But that's my personal preference.

Is there anything "protecting" me from downvotes or something ... properly?

Yes and no. There's nothing protecting you for the specific reason you wrote. But there is a mechanism by which you don't get reputation (positive or negative) for a post. What you can do is click the "community wiki" tickbox on the bottom right of the textfield when you open up your answer for editing. Note that once you make a post a wiki, you cannot turn it back. Making it a wiki lowers the reputation threshold to allow more users to be able to edit your post, and at the same time makes it so that votes on that post no longer affects your reputation.