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

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

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

DELTA = 55/9

DELTA > 0

x = ((55/9)^(1/2)-(-1/3))/(2*(-1/2)) or x = (-(-1/3)-(55/9)^(1/2))/(2*(-1/2))

x = -((55/9)^(1/2)+1/3) or x = (55/9)^(1/2)-1/3

x in { -((55/9)^(1/2)+1/3), (55/9)^(1/2)-1/3}

x in { -((55/9)^(1/2)+1/3), (55/9)^(1/2)-1/3 }

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