x+9/8x+1=x+4/x

Solution for x+9/8x+1=x+4/x equation:

D( x )

x = 0

x = 0

x = 0

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

x+(9/8)*x+1 = x+4/x // - x+4/x

x+(9/8)*x-x-(4/x)+1 = 0

x+(9/8)*x-x-4*x^-1+1 = 0

9/8*x^1-4*x^-1+1*x^0 = 0

(9/8*x^2+1*x^1-4*x^0)/(x^1) = 0 // * x^2

x^1*(9/8*x^2+1*x^1-4*x^0) = 0

x^1

(9/8)*x^2+x-4 = 0

(9/8)*x^2+x-4 = 0

DELTA = 1^2-(-4*4*(9/8))

DELTA = 19

DELTA > 0

x = (19^(1/2)-1)/(2*(9/8)) or x = (-19^(1/2)-1)/(2*(9/8))

x = 4/9*(19^(1/2)-1) or x = -4/9*(19^(1/2)+1)

x in { -4/9*(19^(1/2)+1), 4/9*(19^(1/2)-1)} 

x in { -4/9*(19^(1/2)+1), 4/9*(19^(1/2)-1) }