2/3x-1=5/3-2/x

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Solution for 2/3x-1=5/3-2/x equation: 


D( x )

x = 0

x = 0

x = 0

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

(2/3)*x-1 = 5/3-(2/x) // - 5/3-(2/x)

(2/3)*x+2/x-(5/3)-1 = 0

(2/3)*x+2/x-5/3-1 = 0

2/3*x^1+2*x^-1-8/3*x^0 = 0

(2/3*x^2-8/3*x^1+2*x^0)/(x^1) = 0 // * x^2

x^1*(2/3*x^2-8/3*x^1+2*x^0) = 0

x^1

(2/3)*x^2+(-8/3)*x+2 = 0

(2/3)*x^2+(-8/3)*x+2 = 0

DELTA = (-8/3)^2-(2*4*(2/3))

DELTA = 16/9

DELTA > 0

x = ((16/9)^(1/2)-(-8/3))/(2*(2/3)) or x = (-(-8/3)-(16/9)^(1/2))/(2*(2/3))

x = 3 or x = 1

x in { 1, 3} 

x in { 1, 3 }

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