(5/2x)=(2/x+1)

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Solution for (5/2x)=(2/x+1) equation: 


D( x )

x = 0

x = 0

x = 0

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

(5/2)*x = 2/x+1 // - 2/x+1

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

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

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

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

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

x^1

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

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

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

DELTA = 21

DELTA > 0

x = (21^(1/2)+1)/(2*(5/2)) or x = (1-21^(1/2))/(2*(5/2))

x = (21^(1/2)+1)/5 or x = (1-21^(1/2))/5

x in { (1-21^(1/2))/5, (21^(1/2)+1)/5} 

x in { (1-21^(1/2))/5, (21^(1/2)+1)/5 }

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