x+3/x-6/5x=1/x

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Solution for x+3/x-6/5x=1/x equation: 


D( x )

x = 0

x = 0

x = 0

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

x-((6/5)*x)+3/x = 1/x // - 1/x

x-((6/5)*x)+3/x-(1/x) = 0

x+(-6/5)*x+3/x-x^-1 = 0

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

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

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

x^1

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

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

DELTA = 0^2-(2*4*(-1/5))

DELTA = 8/5

DELTA > 0

x = ((8/5)^(1/2)+0)/(2*(-1/5)) or x = (0-(8/5)^(1/2))/(2*(-1/5))

x = -5/2*(8/5)^(1/2) or x = 5/2*(8/5)^(1/2)

x in { -5/2*(8/5)^(1/2), 5/2*(8/5)^(1/2)} 

x in { -5/2*(8/5)^(1/2), 5/2*(8/5)^(1/2) }

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