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

Solution for 6-1/x-1/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)

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

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

t_1 = x^-1

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

6-t_1^2-t_1 = 0

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

DELTA = 25

DELTA > 0

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

t_1 = -3 or t_1 = 2

t_1 = -3

x^-1+3 = 0

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

x^-1 = -3

-1 < 0

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

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

-1/3 = x^1

x = -1/3

t_1 = 2

x^-1-2 = 0

1*x^-1 = 2 // : 1

x^-1 = 2

-1 < 0

1/(x^1) = 2 // * x^1

1 = 2*x^1 // : 2

1/2 = x^1

x = 1/2

x in { -1/3, 1/2 }