((65/x)+2)*(x-2)=65

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Solution for ((65/x)+2)*(x-2)=65 equation: 


D( x )

x = 0

x = 0

x = 0

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

(65/x+2)*(x-2) = 65 // - 65

(65/x+2)*(x-2)-65 = 0

(65*x^-1+2)*(x-2)-65 = 0

(65*x^-1+2)*(x-2)-65 = 0

2*x-130*x^-1-4 = 0

2*x-130*x^-1-4 = 0

2*(x-65*x^-1-2) = 0

1*x^1-65*x^-1-2*x^0 = 0

(1*x^2-2*x^1-65*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-2*x^1-65*x^0) = 0

x^1

x^2-2*x-65 = 0

x^2-2*x-65 = 0

DELTA = (-2)^2-(-65*1*4)

DELTA = 264

DELTA > 0

x = (264^(1/2)+2)/(1*2) or x = (2-264^(1/2))/(1*2)

x = (2*66^(1/2)+2)/2 or x = (2-2*66^(1/2))/2

x in { (2-2*66^(1/2))/2, (2*66^(1/2)+2)/2} 

2*(x-((2-2*66^(1/2))/2))*(x-((2*66^(1/2)+2)/2)) = 0

2*(x-((2-2*66^(1/2))/2))*(x-((2*66^(1/2)+2)/2)) = 0

( x-((2*66^(1/2)+2)/2) )

x-((2*66^(1/2)+2)/2) = 0 // + (2*66^(1/2)+2)/2

x = (2*66^(1/2)+2)/2

( x-((2-2*66^(1/2))/2) )

x-((2-2*66^(1/2))/2) = 0 // + (2-2*66^(1/2))/2

x = (2-2*66^(1/2))/2

x in { (2*66^(1/2)+2)/2, (2-2*66^(1/2))/2 }

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