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

x^1*(2*x^1-1/5*x^2+2*x^0) = 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 = (-(28/5)^(1/2)-2)/(2*(-1/5))

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

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

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

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