x=2(x+3)/x+5

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Solution for x=2(x+3)/x+5 equation: 


D( x )

x = 0

x = 0

x = 0

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

x = (2*(x+3))/x+5 // - (2*(x+3))/x+5

x-((2*(x+3))/x)-5 = 0

x-2*x^-1*(x+3)-5 = 0

x-2*x^-1*(x+3)-5 = 0

x-6*x^-1-5-2 = 0

x-6*x^-1-7 = 0

x-6*x^-1-7 = 0

1*x^1-6*x^-1-7*x^0 = 0

(1*x^2-7*x^1-6*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-7*x^1-6*x^0) = 0

x^1

x^2-7*x-6 = 0

x^2-7*x-6 = 0

DELTA = (-7)^2-(-6*1*4)

DELTA = 73

DELTA > 0

x = (73^(1/2)+7)/(1*2) or x = (7-73^(1/2))/(1*2)

x = (73^(1/2)+7)/2 or x = (7-73^(1/2))/2

x in { (7-73^(1/2))/2, (73^(1/2)+7)/2} 

(x-((7-73^(1/2))/2))*(x-((73^(1/2)+7)/2)) = 0

(x-((7-73^(1/2))/2))*(x-((73^(1/2)+7)/2)) = 0

( x-((7-73^(1/2))/2) )

x-((7-73^(1/2))/2) = 0 // + (7-73^(1/2))/2

x = (7-73^(1/2))/2

( x-((73^(1/2)+7)/2) )

x-((73^(1/2)+7)/2) = 0 // + (73^(1/2)+7)/2

x = (73^(1/2)+7)/2

x in { (7-73^(1/2))/2, (73^(1/2)+7)/2 }

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