To find T you have to take the integral of dT/dt

First divide both sides by -2 to get

dT/dt = -5+2T Then integrate

T = -5T+T^2+C

if T(0) = 2 then

2 = -5(0)+(0)^2+C

therefore, C = 2

Then, T = -5T+T^2 + 2

Now solve for T by subtracting T to the right side

0 = T^2 - 6T + 2 and solving the quadratic equation

I'll use completing the square method:

T^2 - 6T = -2

(T-3)^2 = -2+9 = 7

T-3 = +/-sqrt(7)

T = 3+/-sqrt(7)

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