Yes, there is a difference!
If f(x) = 21x2 -79x + 30, then -f(x) = -21x2 + 79x - 30!
f(x) opens upward and goes to +∞as |x| goes to ∞, whereas -f(x) opens downward and goes to -≈ as |x| goes to ∞.
BUT, and this is where you are having trouble, if f(x)=0, then -f(x)=0 too, i.e. they have the same roots as you correctly observe.
I hope this helps!