Quadratic Functions and Models

I think i messed up somewhere in this problem, or I'm doing it wrong. Can some please help me figure it out, get me back on track or explain what I did wrong...

The average weight of a sedan could be approximated by

W= 6(t^2) - 240t +4800 (5__<__ t __<__27)

where t is its year of manufacture (t= 0 represents 1970) and W is the average weight of a sedan in pounds. Sketch the graph of W as a function of t. According to the model, in what year were sedans the lightest? What was their average weight in that year?

I have:

W= 6(t^2) - 240t +4800

vertex: (20, 2400)

-b/2a = 240/12 = 20

6(20^2) - 240(20) +4800

= 2400

Then I tried plugging into the quadratic equation to find the x intercepts or roots and I got 54.6 and -14.6