x/3-1/x=2/3

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

DELTA = (-2/3)^2-(-1*4*(1/3))

DELTA = 16/9

DELTA > 0

x = ((16/9)^(1/2)-(-2/3))/(2*(1/3)) or x = (-(-2/3)-(16/9)^(1/2))/(2*(1/3))

x = 3 or x = -1

x in { -1, 3} 

x in { -1, 3 }

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