1/z^2-2/z-15=0

Solution for 1/z^2-2/z-15=0 equation:

D( z )

z^2 = 0

z = 0

z^2 = 0

z^2 = 0

1*z^2 = 0 // : 1

z^2 = 0

z = 0

z = 0

z = 0

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

1/(z^2)-(2/z)-15 = 0

1/(z^2)-2*z^-1-15 = 0

z^-2-2*z^-1-15 = 0

t_1 = z^-1

1*t_1^2-2*t_1^1-15 = 0

t_1^2-2*t_1-15 = 0

DELTA = (-2)^2-(-15*1*4)

DELTA = 64

DELTA > 0

t_1 = (64^(1/2)+2)/(1*2) or t_1 = (2-64^(1/2))/(1*2)

t_1 = 5 or t_1 = -3

t_1 = -3

z^-1+3 = 0

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

z^-1 = -3

-1 < 0

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

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

-1/3 = z^1

z = -1/3

t_1 = 5

z^-1-5 = 0

1*z^-1 = 5 // : 1

z^-1 = 5

-1 < 0

1/(z^1) = 5 // * z^1

1 = 5*z^1 // : 5

1/5 = z^1

z = 1/5

z in { -1/3, 1/5 }