x-6=11/x

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Solution for x-6=11/x equation: 


D( x )

x = 0

x = 0

x = 0

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

x-6 = 11/x // - 11/x

x-(11/x)-6 = 0

x-11*x^-1-6 = 0

1*x^1-11*x^-1-6*x^0 = 0

(1*x^2-6*x^1-11*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-6*x^1-11*x^0) = 0

x^1

x^2-6*x-11 = 0

x^2-6*x-11 = 0

DELTA = (-6)^2-(-11*1*4)

DELTA = 80

DELTA > 0

x = (80^(1/2)+6)/(1*2) or x = (6-80^(1/2))/(1*2)

x = (4*5^(1/2)+6)/2 or x = (6-4*5^(1/2))/2

x in { (6-4*5^(1/2))/2, (4*5^(1/2)+6)/2} 

x in { (6-4*5^(1/2))/2, (4*5^(1/2)+6)/2 }

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