x/6-3/x=1/2

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

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

DELTA = 9/4

DELTA > 0

x = ((9/4)^(1/2)-(-1/2))/(2*(1/6)) or x = (-(-1/2)-(9/4)^(1/2))/(2*(1/6))

x = 6 or x = -3

x in { -3, 6}

x in { -3, 6 }

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