(x-90)/90=140/(x-90+x-50)

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Solution for (x-90)/90=140/(x-90+x-50) equation: 


D( x )

x+x-90-50 = 0

x+x-90-50 = 0

x+x-90-50 = 0

2*x-140 = 0 // + 140

2*x = 140 // : 2

x = 140/2

x = 70

x in (-oo:70) U (70:+oo)

(x-90)/90 = 140/(x+x-90-50) // - 140/(x+x-90-50)

(x-90)/90-(140/(x+x-90-50)) = 0

(x-90)/90-140*(x+x-90-50)^-1 = 0

(x-90)/90-140/(2*x-140) = 0

((x-90)*(2*x-140))/(90*(2*x-140))+(-140*90)/(90*(2*x-140)) = 0

(x-90)*(2*x-140)-140*90 = 0

2*x^2-320*x = 0

2*x^2-320*x = 0

2*x*(x-160) = 0

x-160 = 0 // + 160

x = 160

2*x*(x-160) = 0

(2*x*(x-160))/(90*(2*x-140)) = 0

(2*x*(x-160))/(90*(2*x-140)) = 0 // * 90*(2*x-140)

2*x*(x-160) = 0

( 2*x )

2*x = 0 // : 2

x = 0

( x-160 )

x-160 = 0 // + 160

x = 160

x in { 0, 160 }

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