r = b/2a
Explanation:
We know that force can be derived from potential energy:
F(r) = -dU(r) / dr
=> F(r) = -d/dr (ar² - br + c)
F(r) = -2ar + b
When this force is equal to zero,
F(r) = 0 = -2ar + b
=> 2ar = b
r = b/2a
This is the point where the force goes to zero.