6/2x-9=4/x

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Solution for 6/2x-9=4/x equation: 


D( x )

x = 0

x = 0

x = 0

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

(6/2)*x-9 = 4/x // - 4/x

(6/2)*x-(4/x)-9 = 0

(6/2)*x-4*x^-1-9 = 0

3*x^1-4*x^-1-9*x^0 = 0

(3*x^2-9*x^1-4*x^0)/(x^1) = 0 // * x^2

x^1*(3*x^2-9*x^1-4*x^0) = 0

x^1

3*x^2-9*x-4 = 0

3*x^2-9*x-4 = 0

DELTA = (-9)^2-(-4*3*4)

DELTA = 129

DELTA > 0

x = (129^(1/2)+9)/(2*3) or x = (9-129^(1/2))/(2*3)

x = (129^(1/2)+9)/6 or x = (9-129^(1/2))/6

x in { (9-129^(1/2))/6, (129^(1/2)+9)/6} 

x in { (9-129^(1/2))/6, (129^(1/2)+9)/6 }

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