t = 
multiply both sides by 6rt
6crt = 1 ( divide both sides by 6ct to obtain r )
t = 
"Combinations" isn't really the right word, because a combination doesn't take order of elements into account, and the outcome of a race certainly does depend on order. "Permutations" would be the correct term.
If 4 students are competing, then the race has
4! = 4 • 3 • 2 • 1 = 24
possible outcomes.
The discriminant of this equation is 49. The solutions for this equation are x=2 and x=-

I hope that helps.