8/4x-4=2/x

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


D( x )

x = 0

x = 0

x = 0

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

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

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

(8/4)*x-2*x^-1-4 = 0

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

(2*x^2-4*x^1-2*x^0)/(x^1) = 0 // * x^2

x^1*(2*x^2-4*x^1-2*x^0) = 0

x^1

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

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

DELTA = (-4)^2-(-2*2*4)

DELTA = 32

DELTA > 0

x = (32^(1/2)+4)/(2*2) or x = (4-32^(1/2))/(2*2)

x = (4*2^(1/2)+4)/4 or x = (4-4*2^(1/2))/4

x in { (4-4*2^(1/2))/4, (4*2^(1/2)+4)/4} 

x in { (4-4*2^(1/2))/4, (4*2^(1/2)+4)/4 }

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