x+8/x=9x/k+8

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Solution for x+8/x=9x/k+8 equation: 


D( x )

x = 0

x = 0

x = 0

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

x+8/x = (9*x)/k+8 // - (9*x)/k+8

x-((9*x)/k)+8/x-8 = 0

x-9*k^-1*x+8/x-8 = 0

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

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

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

x^1

x^2-8*x+8 = 0

x^2-8*x+8 = 0

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

DELTA = 32

DELTA > 0

x = (32^(1/2)+8)/(1*2) or x = (8-32^(1/2))/(1*2)

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

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

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

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