(1/y^2)+(2/y)=15

Solution for (1/y^2)+(2/y)=15 equation:

D( y )

y = 0

y^2 = 0

y = 0

y = 0

y^2 = 0

y^2 = 0

1*y^2 = 0 // : 1

y^2 = 0

y = 0

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

2/y+1/(y^2) = 15 // - 15

2/y+1/(y^2)-15 = 0

2*y^-1+y^-2-15 = 0

t_1 = y^-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 = (-64^(1/2)-2)/(1*2)

t_1 = 3 or t_1 = -5

t_1 = -5

y^-1+5 = 0

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

y^-1 = -5

-1 < 0

1/(y^1) = -5 // * y^1

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

-1/5 = y^1

y = -1/5

t_1 = 3

y^-1-3 = 0

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

y^-1 = 3

-1 < 0

1/(y^1) = 3 // * y^1

1 = 3*y^1 // : 3

1/3 = y^1

y = 1/3

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