x-8/x-4=2

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Solution for x-8/x-4=2 equation: 


D( x )

x = 0

x = 0

x = 0

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

x-(8/x)-4 = 2 // - 2

x-(8/x)-4-2 = 0

x-8*x^-1-4-2 = 0

1*x^1-8*x^-1-6*x^0 = 0

(1*x^2-6*x^1-8*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-6*x^1-8*x^0) = 0

x^1

x^2-6*x-8 = 0

x^2-6*x-8 = 0

DELTA = (-6)^2-(-8*1*4)

DELTA = 68

DELTA > 0

x = (68^(1/2)+6)/(1*2) or x = (6-68^(1/2))/(1*2)

x = (2*17^(1/2)+6)/2 or x = (6-2*17^(1/2))/2

x in { (6-2*17^(1/2))/2, (2*17^(1/2)+6)/2} 

x in { (6-2*17^(1/2))/2, (2*17^(1/2)+6)/2 }

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