1-6/x-27/x^2=0

Solution for 1-6/x-27/x^2=0 equation:

D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

1-(6/x)-(27/(x^2)) = 0

1-6*x^-1-27*x^-2 = 0

t_1 = x^-1

1-27*t_1^2-6*t_1^1 = 0

1-27*t_1^2-6*t_1 = 0

DELTA = (-6)^2-(-27*1*4)

DELTA = 144

DELTA > 0

t_1 = (144^(1/2)+6)/(-27*2) or t_1 = (6-144^(1/2))/(-27*2)

t_1 = -1/3 or t_1 = 1/9

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 = 1/9

x^-1-1/9 = 0

1*x^-1 = 1/9 // : 1

x^-1 = 1/9

-1 < 0

1/(x^1) = 1/9 // * x^1

1 = 1/9*x^1 // : 1/9

9 = x^1

x = 9

x in { -3, 9 }