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I'd want to get perspective on what I feel is an unjustified case of academic misconduct.

I am taking a mathematics subject and part of my assignment was to submit answers to questions given.

One of the questions I was unsure of what method I should apply, I searched on youtube and found tutorials on how to solve this problem. I should make it explicit the direct answer was not part of the video, however, using the same method I could substitute my values and get the correct answer.

I may be accused of plagiarism and apparently, my use of the video was unfair and plagiarism. I suspect it's because I used the same symbols which in retrospect I could have, should have changed however I still feel this is unjustified and comparable to applying the chain rule or any other mathematical principle taught through the increasingly powerful use of the internet.

Do you think there are ground to challenge this? I thought I was doing my due diligence sourcing methods, not direct answers.

Do you think this fair?

Whatever it was, it wasn't plagiarism. Whether it was within the rules set by your professor is another question. But, assuming that the rules permitted online research to answer the question, then that is all you did. You will have to judge conformance to the rules of your course.

If someone has accused you of plagiarism they are probably using the word incorrectly. That doesn't mean, of course, that you aren't without fault. That is for you and others to judge.

Using the same symbols in mathematics can hardly be faulted in any case, as many of them are standardized and used in the same way throughout mathematics. They might, however, have been a tip-off that you went outside the allowed bounds.

But, for your own educational progress, I hope you don't go to the web too soon to get such questions answered. Struggling with a problem expands your mind in a way very different from finding a solution or a solution framework. If you want to be a mathematician, you need to develop that skill.

Note that exercises given in almost every course, aren't given for the purpose of finding an answer. The professor already has the answer. The purpose is to help you grow your mental abilities. Work on the hard problems. If you want to learn more, work on harder problems.

...I was unsure of what method I should apply, I searched on youtube and found tutorials on how to solve this problem...using the same method I could substitute my values and get the correct answer.

That is not plagiarism, that is learning: You were given a problem, you found a method that could be used to solve your problem, and you applied the method to your problem. That's exactly how we learn.

By analogy, suppose I'm asked to find the area of a circle, but I don't know how. So, I search the internet and discover that the area of a circle is π·r². Now I'm able to apply what I've learnt to solve the problem (assuming I know the radius r or diameter 2·r). That's how we learn, that's not plagiarism.

I concur with @user2768 's answer. What you did was fine, unless the assignment specified "don't look anything up".

I think what you should have done was include in your submission exactly what you told us here:

I was unsure of what method I should apply, I searched on youtube and
found tutorials on how to solve this problem.

with a reference to the link that helped you.

Had you done so the worst case would be an accusation that you misinterpreted the rules (which may not have been clearly stated), not that you cheated in any way.

This is what I provide my students for guidance: https://www.cs.umb.edu/~eb/honesty/