3/x-2-1/x=1/5x

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Solution for 3/x-2-1/x=1/5x equation: 


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

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

DELTA = 28/5

DELTA > 0

x = ((28/5)^(1/2)+2)/(2*(-1/5)) or x = (2-(28/5)^(1/2))/(2*(-1/5))

x = -5/2*((28/5)^(1/2)+2) or x = -5/2*(2-(28/5)^(1/2))

x in { -5/2*((28/5)^(1/2)+2), -5/2*(2-(28/5)^(1/2))} 

x in { -5/2*((28/5)^(1/2)+2), -5/2*(2-(28/5)^(1/2)) }

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