3=13/z+10/z^2

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Solution for 3=13/z+10/z^2 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)

3 = 13/z+10/(z^2) // - 13/z+10/(z^2)

3-(13/z)-(10/(z^2)) = 0

3-13*z^-1-10*z^-2 = 0

t_1 = z^-1

3-10*t_1^2-13*t_1^1 = 0

3-10*t_1^2-13*t_1 = 0

DELTA = (-13)^2-(-10*3*4)

DELTA = 289

DELTA > 0

t_1 = (289^(1/2)+13)/(-10*2) or t_1 = (13-289^(1/2))/(-10*2)

t_1 = -3/2 or t_1 = 1/5

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

t_1 = 1/5

z^-1-1/5 = 0

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

z^-1 = 1/5

-1 < 0

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

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

5 = z^1

z = 5

z in { -2/3, 5 }

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