(1/x)-(1/3x)=(1/6)

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Solution for (1/x)-(1/3x)=(1/6) equation: 


D( x )

x = 0

x = 0

x = 0

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

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

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

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

1*x^-1-1/3*x^1-1/6*x^0 = 0

(1*x^0-1/3*x^2-1/6*x^1)/(x^1) = 0 // * x^2

x^1*(1*x^0-1/3*x^2-1/6*x^1) = 0

x^1

(-1/3)*x^2+(-1/6)*x+1 = 0

(-1/3)*x^2+(-1/6)*x+1 = 0

DELTA = (-1/6)^2-(1*4*(-1/3))

DELTA = 49/36

DELTA > 0

x = ((49/36)^(1/2)-(-1/6))/(2*(-1/3)) or x = (-(-1/6)-(49/36)^(1/2))/(2*(-1/3))

x = -2 or x = 3/2

x in { -2, 3/2} 

x in { -2, 3/2 }

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