2-3/y=5/y^2

Solution for 2-3/y=5/y^2 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-(3/y) = 5/(y^2) // - 5/(y^2)

2-(3/y)-(5/(y^2)) = 0

2-3*y^-1-5*y^-2 = 0

t_1 = y^-1

2-5*t_1^2-3*t_1^1 = 0

2-5*t_1^2-3*t_1 = 0

DELTA = (-3)^2-(-5*2*4)

DELTA = 49

DELTA > 0

t_1 = (49^(1/2)+3)/(-5*2) or t_1 = (3-49^(1/2))/(-5*2)

t_1 = -1 or t_1 = 2/5

t_1 = -1

y^-1+1 = 0

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

y^-1 = -1

-1 < 0

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

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

-1 = y^1

y = -1

t_1 = 2/5

y^-1-2/5 = 0

1*y^-1 = 2/5 // : 1

y^-1 = 2/5

-1 < 0

1/(y^1) = 2/5 // * y^1

1 = 2/5*y^1 // : 2/5

5/2 = y^1

y = 5/2

y in { -1, 5/2 }