There aren't that many possibilities for n, so you could use brute force and just check them all.
This is in a section on number theory. Perhaps you can find some divisibility relationship between \(n^2 + 9n -2\) and the total number of people.
Think about factoring \(n^2 + 9n -2\). Perhaps with a remainder left over. What smaller polynomial might you want to factor out of it?
When you write up your answer, your example or proof should be related back to the original problem. So it should mention muffins and people, rather than consisting only of equations.