Melody: Hi Tayfuntan,
One source of confusion is that t and T are totally different things
T is a constant and t is a variable.
131222 Latex answer integral.JPG
I then used Wolfram Alpha calculator to solve
http://www.wolframalpha.com/input/?i=solve+%2836.4%2B6*10%5E-3T-2*10%5E5*T%5E-2%29%28T-600%29+%3D94258+over+the+real+numbers
There are 4 answers.