The 'c' in your equation is the 'x' in this one, the weird +- sign means that you gotta calculate it once for + and once for - (there's usually 2 answers to quadratic equations that's why). The a,b and c in this formula are the factors in front of your variable so 'a' is the first one in front on the c^2, b is the one in front of just the c and 'c' in the formula would be the third one which would then be alone without a variable but you don't have that in your equation so just write '0' where there's a 'c' in this formula.
\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
15c2 - 10c = 0
5c(3c - 2) = 0
Either 5c = 0 or 3c - 2 = 0
c = 0 3c = 2
c = 2/3
You broke one of the rules. You divided by the variable as long as you don't know what that variable is it might as well be 0 so you divided by 0 congrats. Just kidding. You're right in this case but you didn't try to use the formula you simply saw a relationship between 15 and 10 right away.
If the equation was 1/576c^2-17c=0 the problem would be of the same nature but you couldn't solve it that fast the way you did so i really suggest learning how to make use of this \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)if you wanna get a good grade with the coming maths exam.