2/3x=6/x-3

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

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

DELTA = 25

DELTA > 0

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

x = 3/2 or x = -6

x in { -6, 3/2} 

x in { -6, 3/2 }

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