1/6*x^(-2)-5/6*x^(-1)+1

Solution for 1/6*x^(-2)-5/6*x^(-1)+1 equation:

D( x )

x = 0

x = 0

x = 0

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

(1/6)*x^-2-((5/6)*x^-1)+1 = 0

(-5/6)*x^-1+(1/6)*x^-2+1 = 0

1/6*x^-2-5/6*x^-1+1 = 0

t_1 = x^-1

1/6*t_1^2-5/6*t_1^1+1 = 0

1/6*t_1^2-5/6*t_1+1 = 0

DELTA = (-5/6)^2-(1/6*1*4)

DELTA = 1/36

DELTA > 0

t_1 = ((1/36)^(1/2)+5/6)/(1/6*2) or t_1 = (5/6-(1/36)^(1/2))/(1/6*2)

t_1 = 3 or t_1 = 2

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

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

x in { 1/2, 1/3 }