6/9=x-4/x

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Solution for 6/9=x-4/x equation: 


D( x )

x = 0

x = 0

x = 0

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

6/9 = x-(4/x) // - x-(4/x)

4/x-x+6/9 = 0

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

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

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

x^1

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

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

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

DELTA = 148/9

DELTA > 0

x = ((148/9)^(1/2)-(2/3))/(-1*2) or x = (-(2/3)-(148/9)^(1/2))/(-1*2)

x = ((148/9)^(1/2)-2/3)/(-2) or x = ((148/9)^(1/2)+2/3)/2

x in { ((148/9)^(1/2)-2/3)/(-2), ((148/9)^(1/2)+2/3)/2} 

x in { ((148/9)^(1/2)-2/3)/(-2), ((148/9)^(1/2)+2/3)/2 }

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