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

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Solution for 6/x-1/2=3/2x equation: 


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

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

DELTA = 145/4

DELTA > 0

x = ((145/4)^(1/2)-(-1/2))/(2*(-3/2)) or x = (-(-1/2)-(145/4)^(1/2))/(2*(-3/2))

x = ((145/4)^(1/2)+1/2)/(-3) or x = (1/2-(145/4)^(1/2))/(-3)

x in { ((145/4)^(1/2)+1/2)/(-3), (1/2-(145/4)^(1/2))/(-3)} 

x in { ((145/4)^(1/2)+1/2)/(-3), (1/2-(145/4)^(1/2))/(-3) }

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