180/(x-6)-180/x=1.5

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Solution for 180/(x-6)-180/x=1.5 equation: 


D( x )

x-6 = 0

x = 0

x-6 = 0

x-6 = 0

x-6 = 0 // + 6

x = 6

x = 0

x = 0

x in (-oo:0) U (0:6) U (6:+oo)

180/(x-6)-(180/x) = 1.5 // - 1.5

180/(x-6)-(180/x)-1.5 = 0

180/(x-6)-180*x^-1-1.5 = 0

180/(x-6)-180/x-1.5 = 0

(180*x)/(x*(x-6))+(-180*(x-6))/(x*(x-6))+(-1.5*x*(x-6))/(x*(x-6)) = 0

180*x-180*(x-6)-1.5*x*(x-6) = 0

9*x-1.5*x^2+1080 = 0

9*x-1.5*x^2+1080 = 0

9*x-1.5*x^2+1080 = 0

DELTA = 9^2-(-1.5*4*1080)

DELTA = 6561

DELTA > 0

x = (6561^(1/2)-9)/(-1.5*2) or x = (-6561^(1/2)-9)/(-1.5*2)

x = -24 or x = 30

(x+24)*(x-30) = 0

((x+24)*(x-30))/(x*(x-6)) = 0

((x+24)*(x-30))/(x*(x-6)) = 0 // * x*(x-6)

(x+24)*(x-30) = 0

( x+24 )

x+24 = 0 // - 24

x = -24

( x-30 )

x-30 = 0 // + 30

x = 30

x in { -24, 30 }

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