(x-8/3x)+9=(x+6/x)

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Solution for (x-8/3x)+9=(x+6/x) equation: 


D( x )

x = 0

x = 0

x = 0

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

x-((8/3)*x)+9 = x+6/x // - x+6/x

x-((8/3)*x)-x-(6/x)+9 = 0

x+(-8/3)*x-x-6*x^-1+9 = 0

9*x^0-8/3*x^1-6*x^-1 = 0

(9*x^1-8/3*x^2-6*x^0)/(x^1) = 0 // * x^2

x^1*(9*x^1-8/3*x^2-6*x^0) = 0

x^1

(-8/3)*x^2+9*x-6 = 0

(-8/3)*x^2+9*x-6 = 0

DELTA = 9^2-(-6*4*(-8/3))

DELTA = 17

DELTA > 0

x = (17^(1/2)-9)/(2*(-8/3)) or x = (-17^(1/2)-9)/(2*(-8/3))

x = -3/16*(17^(1/2)-9) or x = 3/16*(17^(1/2)+9)

x in { -3/16*(17^(1/2)-9), 3/16*(17^(1/2)+9)} 

x in { -3/16*(17^(1/2)-9), 3/16*(17^(1/2)+9) }

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