x^-2-x^-1=4/9

Solution for x^-2-x^-1=4/9 equation:

D( x )

x = 0

x = 0

x = 0

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

x^-2-x^-1 = 4/9 // - 4/9

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

x^-2-x^-1-4/9 = 0

t_1 = x^-1

1*t_1^2-1*t_1^1-4/9 = 0

t_1^2-t_1-4/9 = 0

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

DELTA = 25/9

DELTA > 0

t_1 = ((25/9)^(1/2)+1)/(1*2) or t_1 = (1-(25/9)^(1/2))/(1*2)

t_1 = 4/3 or t_1 = -1/3

t_1 = -1/3

x^-1+1/3 = 0

1*x^-1 = -1/3 // : 1

x^-1 = -1/3

-1 < 0

1/(x^1) = -1/3 // * x^1

1 = -1/3*x^1 // : -1/3

-3 = x^1

x = -3

t_1 = 4/3

x^-1-4/3 = 0

1*x^-1 = 4/3 // : 1

x^-1 = 4/3

-1 < 0

1/(x^1) = 4/3 // * x^1

1 = 4/3*x^1 // : 4/3

3/4 = x^1

x = 3/4

x in { -3, 3/4 }