x-9=27/x

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Solution for x-9=27/x equation: 


D( x )

x = 0

x = 0

x = 0

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

x-9 = 27/x // - 27/x

x-(27/x)-9 = 0

x-27*x^-1-9 = 0

1*x^1-27*x^-1-9*x^0 = 0

(1*x^2-9*x^1-27*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-9*x^1-27*x^0) = 0

x^1

x^2-9*x-27 = 0

x^2-9*x-27 = 0

DELTA = (-9)^2-(-27*1*4)

DELTA = 189

DELTA > 0

x = (189^(1/2)+9)/(1*2) or x = (9-189^(1/2))/(1*2)

x = (3*21^(1/2)+9)/2 or x = (9-3*21^(1/2))/2

x in { (9-3*21^(1/2))/2, (3*21^(1/2)+9)/2} 

x in { (9-3*21^(1/2))/2, (3*21^(1/2)+9)/2 }

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