(16/4x-4)=(4/x)

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Solution for (16/4x-4)=(4/x) equation: 


D( x )

x = 0

x = 0

x = 0

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

(16/4)*x-4 = 4/x // - 4/x

(16/4)*x-(4/x)-4 = 0

(16/4)*x-4*x^-1-4 = 0

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

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

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

x^1

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

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

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

DELTA = 80

DELTA > 0

x = (80^(1/2)+4)/(2*4) or x = (4-80^(1/2))/(2*4)

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

x in { (4-4*5^(1/2))/8, (4*5^(1/2)+4)/8} 

x in { (4-4*5^(1/2))/8, (4*5^(1/2)+4)/8 }

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