(x+4/9x)+1=(x+9/x)

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Solution for (x+4/9x)+1=(x+9/x) equation: 


D( x )

x = 0

x = 0

x = 0

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

x+(4/9)*x+1 = x+9/x // - x+9/x

x+(4/9)*x-x-(9/x)+1 = 0

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

4/9*x^1-9*x^-1+1*x^0 = 0

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

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

x^1

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

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

DELTA = 1^2-(-9*4*(4/9))

DELTA = 17

DELTA > 0

x = (17^(1/2)-1)/(2*(4/9)) or x = (-17^(1/2)-1)/(2*(4/9))

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

x in { -9/8*(17^(1/2)+1), 9/8*(17^(1/2)-1)} 

x in { -9/8*(17^(1/2)+1), 9/8*(17^(1/2)-1) }

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