x-5=10/x

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Solution for x-5=10/x equation: 


D( x )

x = 0

x = 0

x = 0

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

x-5 = 10/x // - 10/x

x-(10/x)-5 = 0

x-10*x^-1-5 = 0

1*x^1-10*x^-1-5*x^0 = 0

(1*x^2-5*x^1-10*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-5*x^1-10*x^0) = 0

x^1

x^2-5*x-10 = 0

x^2-5*x-10 = 0

DELTA = (-5)^2-(-10*1*4)

DELTA = 65

DELTA > 0

x = (65^(1/2)+5)/(1*2) or x = (5-65^(1/2))/(1*2)

x = (65^(1/2)+5)/2 or x = (5-65^(1/2))/2

x in { (5-65^(1/2))/2, (65^(1/2)+5)/2} 

x in { (5-65^(1/2))/2, (65^(1/2)+5)/2 }

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