2x=3/x-1/6

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

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

DELTA = 865/36

DELTA > 0

x = ((865/36)^(1/2)-(1/6))/(2*2) or x = (-(1/6)-(865/36)^(1/2))/(2*2)

x = ((865/36)^(1/2)-1/6)/4 or x = (-((865/36)^(1/2)+1/6))/4

x in { (-((865/36)^(1/2)+1/6))/4, ((865/36)^(1/2)-1/6)/4}

x in { (-((865/36)^(1/2)+1/6))/4, ((865/36)^(1/2)-1/6)/4 }

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