120000/(1+48e^-0.015x)=24e^0.055x

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Solution for 120000/(1+48e^-0.015x)=24e^0.055x equation: 


D( x )

48*e^-0.015*x+1 = 0

48*e^-0.015*x+1 = 0

48*e^-0.015*x+1 = 0

48*e^-0.015*x+1 = 0 // - 1

48*e^-0.015*x = -1 // : 48*e^-0.015

x = -1/(48*e^-0.015)

x in (-oo:-1/(48*e^-0.015)) U (-1/(48*e^-0.015):+oo)

120000/(48*e^-0.015*x+1) = 24*e^0.055*x // - 24*e^0.055*x

120000/(48*e^-0.015*x+1)-(24*e^0.055*x) = 0

120000/(48*e^-0.015*x+1)-24*e^0.055*x = 0

120000/(48*e^-0.015*x+1)+(-24*e^0.055*x*(48*e^-0.015*x+1))/(48*e^-0.015*x+1) = 0

120000-24*e^0.055*x*(48*e^-0.015*x+1) = 0

120000-1152*e^0.04*x^2-24*e^0.055*x = 0

120000-1152*e^0.04*x^2-24*e^0.055*x = 0

120000-1152*e^0.04*x^2-24*e^0.055*x = 0

DELTA = (-24*e^0.055)^2-(-1152*4*120000*e^0.04)

DELTA = 576*e^0.11+552960000*e^0.04

DELTA = 575527366.35536832

DELTA > 0

x = ((576*e^0.11+552960000*e^0.04)^(1/2)-(-24*e^0.055))/(-1152*2*e^0.04) or x = (-(-24*e^0.055)-(576*e^0.11+552960000*e^0.04)^(1/2))/(-1152*2*e^0.04)

x = (24*e^0.055+(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04) or x = (24*e^0.055-(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04)

(x-((24*e^0.055+(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04)))*(x-((24*e^0.055-(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04))) = 0

((x-((24*e^0.055+(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04)))*(x-((24*e^0.055-(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04))))/(48*e^-0.015*x+1) = 0

((x-((24*e^0.055+(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04)))*(x-((24*e^0.055-(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04))))/(48*e^-0.015*x+1) = 0 // * 48*e^-0.015*x+1

(x-((24*e^0.055+(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04)))*(x-((24*e^0.055-(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04))) = 0

( x-((24*e^0.055+(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04)) )

x-((24*e^0.055+(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04)) = 0 // + (24*e^0.055+(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04)

x = (24*e^0.055+(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04)

( x-((24*e^0.055-(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04)) )

x-((24*e^0.055-(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04)) = 0 // + (24*e^0.055-(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04)

x = (24*e^0.055-(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04)

x in { (24*e^0.055+(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04), (24*e^0.055-(576*e^0.11+552960000*e^0.04)^(1/2))/(-2304*e^0.04) }

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