1-8/x-33/x^2=0

Solution for 1-8/x-33/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-(8/x)-(33/(x^2)) = 0

1-8*x^-1-33*x^-2 = 0

t_1 = x^-1

1-33*t_1^2-8*t_1^1 = 0

1-33*t_1^2-8*t_1 = 0

DELTA = (-8)^2-(-33*1*4)

DELTA = 196

DELTA > 0

t_1 = (196^(1/2)+8)/(-33*2) or t_1 = (8-196^(1/2))/(-33*2)

t_1 = -1/3 or t_1 = 1/11

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 = 1/11

x^-1-1/11 = 0

1*x^-1 = 1/11 // : 1

x^-1 = 1/11

-1 < 0

1/(x^1) = 1/11 // * x^1

1 = 1/11*x^1 // : 1/11

11 = x^1

x = 11

x in { -3, 11 }