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D( t )
t-5 = 0
t-5 = 0
t-5 = 0
t-5 = 0 // + 5
t = 5
t in (-oo:5) U (5:+oo)
(t/(t-5))^2-((2*t)/(t-5))-8 = 0
(t/(t-5))^2-2*t*(t-5)^-1-8 = 0
(t^2)/((t-5)^2)+(-2*t)/(t-5)-8 = 0
(t^2)/((t-5)^2)+(-2*t*(t-5))/((t-5)^2)+(-8*(t-5)^2)/((t-5)^2) = 0
t^2-2*t*(t-5)-8*(t-5)^2 = 0
10*t-t^2-8*t^2+80*t-200 = 0
90*t-9*t^2-200 = 0
90*t-9*t^2-200 = 0
90*t-9*t^2-200 = 0
DELTA = 90^2-(-200*(-9)*4)
DELTA = 900
DELTA > 0
t = (900^(1/2)-90)/(-9*2) or t = (-900^(1/2)-90)/(-9*2)
t = 10/3 or t = 20/3
(t-10/3)*(t-20/3) = 0
((t-10/3)*(t-20/3))/((t-5)^2) = 0
((t-10/3)*(t-20/3))/((t-5)^2) = 0 // * (t-5)^2
(t-10/3)*(t-20/3) = 0
( t-10/3 )
t-10/3 = 0 // + 10/3
t = 10/3
( t-20/3 )
t-20/3 = 0 // + 20/3
t = 20/3
t in { 10/3, 20/3 }
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