Solution:

The equation is equal to $$(2x-(a+c))(x-b)$$$$= 2(x-b)\left(x- \dfrac{a+c}2\right).$$ This makes the roots equal to: $$b,\dfrac{a+c}2$$ and the sum is $$\dfrac{2b+a+c}2.$$

Therefore, we want to maximize $a,b,c,$ while making $b$ the highest.

As such, we can have $b=9,a=8,c=7$ and get a sum: $$9+7.5=16.5$$

Thus, the correct answer is D .