500=200(1-t/20)^2

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Solution for 500=200(1-t/20)^2 equation: 


t in (-oo:+oo)

500 = 200*(1-(t/20))^2 // - 200*(1-(t/20))^2

500-(200*(1-(t/20))^2) = 0

500-200*(1-(t/20))^2 = 0

500-200*(1-1/20*t)^2 = 0

500-200*(1-1/20*t)^2 = 0

20*t-1/2*t^2+300 = 0

20*t-1/2*t^2+300 = 0

20*t-1/2*t^2+300 = 0

DELTA = 20^2-(-1/2*4*300)

DELTA = 1000

DELTA > 0

t = (1000^(1/2)-20)/(-1/2*2) or t = (-1000^(1/2)-20)/(-1/2*2)

t = 20-(10*10^(1/2)) or t = 20-(-10*10^(1/2))

(t+10*10^(1/2)-20)*(t-10*10^(1/2)-20) = 0

(t+10*10^(1/2)-20)*(t-10*10^(1/2)-20) = 0

( t+10*10^(1/2)-20 )

t+10*10^(1/2)-20 = 0 // - 10*10^(1/2)-20

t = -(10*10^(1/2)-20)

t = 20-(10*10^(1/2))

( t-10*10^(1/2)-20 )

t-10*10^(1/2)-20 = 0 // + -10*10^(1/2)-20

t = -(-10*10^(1/2)-20)

t = 20-(-10*10^(1/2))

t in { 20-(10*10^(1/2)), 20-(-10*10^(1/2)) }

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