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

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

3/2*x^1-4*x^-1-5/3*x^0 = 0

(3/2*x^2-5/3*x^1-4*x^0)/(x^1) = 0 // * x^2

x^1*(3/2*x^2-5/3*x^1-4*x^0) = 0

x^1

(3/2)*x^2+(-5/3)*x-4 = 0

(3/2)*x^2+(-5/3)*x-4 = 0

DELTA = (-5/3)^2-(-4*4*(3/2))

DELTA = 241/9

DELTA > 0

x = ((241/9)^(1/2)-(-5/3))/(2*(3/2)) or x = (-(-5/3)-(241/9)^(1/2))/(2*(3/2))

x = ((241/9)^(1/2)+5/3)/3 or x = (5/3-(241/9)^(1/2))/3

x in { (5/3-(241/9)^(1/2))/3, ((241/9)^(1/2)+5/3)/3} 

x in { (5/3-(241/9)^(1/2))/3, ((241/9)^(1/2)+5/3)/3 }

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