8/2x-4=5/x

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Solution for 8/2x-4=5/x equation: 


D( x )

x = 0

x = 0

x = 0

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

(8/2)*x-4 = 5/x // - 5/x

(8/2)*x-(5/x)-4 = 0

(8/2)*x-5*x^-1-4 = 0

4*x^1-5*x^-1-4*x^0 = 0

(4*x^2-4*x^1-5*x^0)/(x^1) = 0 // * x^2

x^1*(4*x^2-4*x^1-5*x^0) = 0

x^1

4*x^2-4*x-5 = 0

4*x^2-4*x-5 = 0

DELTA = (-4)^2-(-5*4*4)

DELTA = 96

DELTA > 0

x = (96^(1/2)+4)/(2*4) or x = (4-96^(1/2))/(2*4)

x = (4*6^(1/2)+4)/8 or x = (4-4*6^(1/2))/8

x in { (4-4*6^(1/2))/8, (4*6^(1/2)+4)/8} 

x in { (4-4*6^(1/2))/8, (4*6^(1/2)+4)/8 }

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