1-(1/6z^-1)-(1/3z^-2)

Solution for 1-(1/6z^-1)-(1/3z^-2) equation:

D( z )

z = 0

z = 0

z = 0

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

1-((1/6)*z^-1)-((1/3)*z^-2) = 0

(-1/6)*z^-1+(-1/3)*z^-2+1 = 0

1-1/6*z^-1-1/3*z^-2 = 0

t_1 = z^-1

1-1/3*t_1^2-1/6*t_1^1 = 0

1-1/3*t_1^2-1/6*t_1 = 0

DELTA = (-1/6)^2-(-1/3*1*4)

DELTA = 49/36

DELTA > 0

t_1 = ((49/36)^(1/2)+1/6)/(-1/3*2) or t_1 = (1/6-(49/36)^(1/2))/(-1/3*2)

t_1 = -2 or t_1 = 3/2

t_1 = -2

z^-1+2 = 0

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

z^-1 = -2

-1 < 0

1/(z^1) = -2 // * z^1

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

-1/2 = z^1

z = -1/2

t_1 = 3/2

z^-1-3/2 = 0

1*z^-1 = 3/2 // : 1

z^-1 = 3/2

-1 < 0

1/(z^1) = 3/2 // * z^1

1 = 3/2*z^1 // : 3/2

2/3 = z^1

z = 2/3

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