x-3/2x=x-5/x

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Solution for x-3/2x=x-5/x equation: 


D( x )

x = 0

x = 0

x = 0

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

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

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

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

5*x^-1-3/2*x^1 = 0

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

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

x^1

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

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

DELTA = 0^2-(4*5*(-3/2))

DELTA = 30

DELTA > 0

x = (30^(1/2)+0)/(2*(-3/2)) or x = (0-30^(1/2))/(2*(-3/2))

x = (30^(1/2))/(-3) or x = (30^(1/2))/3

x in { (30^(1/2))/(-3), (30^(1/2))/3} 

x in { (30^(1/2))/(-3), (30^(1/2))/3 }

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