3/x-1/2x=1/2

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

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

DELTA = 25/4

DELTA > 0

x = ((25/4)^(1/2)-(-1/2))/(2*(-1/2)) or x = (-(-1/2)-(25/4)^(1/2))/(2*(-1/2))

x = -3 or x = 2

x in { -3, 2} 

x in { -3, 2 }

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