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t in (-oo:+oo)
500 = 2000*(1-(t/20))^2 // - 2000*(1-(t/20))^2
500-(2000*(1-(t/20))^2) = 0
500-2000*(1-(t/20))^2 = 0
500-2000*(1-1/20*t)^2 = 0
500-2000*(1-1/20*t)^2 = 0
200*t-5*t^2-1500 = 0
200*t-5*t^2-1500 = 0
5*(40*t-t^2-300) = 0
40*t-t^2-300 = 0
DELTA = 40^2-(-300*(-1)*4)
DELTA = 400
DELTA > 0
t = (400^(1/2)-40)/(-1*2) or t = (-400^(1/2)-40)/(-1*2)
t = 10 or t = 30
5*(t-10)*(t-30) = 0
5*(t-10)*(t-30) = 0
( t-10 )
t-10 = 0 // + 10
t = 10
( t-30 )
t-30 = 0 // + 30
t = 30
t in { 10, 30 }
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