A lot of people are telling you to check whether your idea really is novel. You should probably do that, but even if you find out that someone else has already published it, not all is lost.

If your derivation is different (hopefully simpler) and you do additional analysis (e.g. of numerical stability), you could still get a publication out of it. (Probably not in a top journal, but better than a paper mill.)

Disclaimer: I have not published any papers myself, but I have read papers that were essentially "The method presented in X et al. is useful, but we didn't get the explanation until we rediscovered it ourselves. Here is a more understandable derivation.".

Great goals, as others suggested: depending on what side of the field it falls to, post to https://cs.stackexchange.com/ or https://mathoverflow.net/ and ask for help improving and whether it's original and mention you'd like to publish although the latter is off topic there. Or you can try to email me at chx1975 gmail and I will ask my high school classmates whether they know anyone who would be helpful. They will. It was that sort of high school. Some became very high level game developers some became lecturers and associate professors and so on.