4/6x-1/x=1/3

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Solution for 4/6x-1/x=1/3 equation: 


D( x )

x = 0

x = 0

x = 0

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

(4/6)*x-(1/x) = 1/3 // - 1/3

(4/6)*x-(1/x)-(1/3) = 0

(4/6)*x-x^-1-1/3 = 0

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

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

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

x^1

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

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

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

DELTA = 25/9

DELTA > 0

x = ((25/9)^(1/2)-(-1/3))/(2*(2/3)) or x = (-(-1/3)-(25/9)^(1/2))/(2*(2/3))

x = 3/2 or x = -1

x in { -1, 3/2} 

x in { -1, 3/2 }

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