SOLUTION: The number of people infected after t days is P = 200 + 5t - t2. Find the number of days until the number of people infected is 150.

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P = 200 + 5t - t^2
The problem gives you:
P = 150
150 = 200 + 5t - t^2
Moving everything to the left:
t^2 - 5t - 200 + 150 = 0
t^2 - 5t - 50 = 0
(t-10)(t+5) = 0
.
t = {-5, 10}
Tossing out the negative solution we are left with:
t = 10 days