2/3x-2=1/x-4

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Solution for 2/3x-2=1/x-4 equation:


D( x )

x = 0

x = 0

x = 0

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

(2/3)*x-2 = 1/x-4 // - 1/x-4

(2/3)*x-(1/x)-2+4 = 0

(2/3)*x-x^-1-2+4 = 0

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

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

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

x^1

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

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

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

DELTA = 20/3

DELTA > 0

x = ((20/3)^(1/2)-2)/(2*(2/3)) or x = (-(20/3)^(1/2)-2)/(2*(2/3))

x = 3/4*((20/3)^(1/2)-2) or x = -3/4*((20/3)^(1/2)+2)

x in { -3/4*((20/3)^(1/2)+2), 3/4*((20/3)^(1/2)-2)}

x in { -3/4*((20/3)^(1/2)+2), 3/4*((20/3)^(1/2)-2) }

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