(4/9x+9)=(6/x+1)-(5/9)

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Solution for (4/9x+9)=(6/x+1)-(5/9) equation: 


D( x )

x = 0

x = 0

x = 0

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

(4/9)*x+9 = 6/x-(5/9)+1 // - 6/x-(5/9)+1

(4/9)*x-(6/x)+5/9-1+9 = 0

(4/9)*x-6*x^-1+5/9-1+9 = 0

4/9*x^1-6*x^-1+77/9*x^0 = 0

(4/9*x^2+77/9*x^1-6*x^0)/(x^1) = 0 // * x^2

x^1*(4/9*x^2+77/9*x^1-6*x^0) = 0

x^1

(4/9)*x^2+(77/9)*x-6 = 0

(4/9)*x^2+(77/9)*x-6 = 0

DELTA = (77/9)^2-(-6*4*(4/9))

DELTA = 6793/81

DELTA > 0

x = ((6793/81)^(1/2)-(77/9))/(2*(4/9)) or x = (-(77/9)-(6793/81)^(1/2))/(2*(4/9))

x = 9/8*((6793/81)^(1/2)-77/9) or x = -9/8*((6793/81)^(1/2)+77/9)

x in { -9/8*((6793/81)^(1/2)+77/9), 9/8*((6793/81)^(1/2)-77/9)} 

x in { -9/8*((6793/81)^(1/2)+77/9), 9/8*((6793/81)^(1/2)-77/9) }

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