(y-15/y)^2-12(y-15/y)-28=0

Solution for (y-15/y)^2-12(y-15/y)-28=0 equation:

D( y )

y = 0

y = 0

y = 0

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

(y-(15/y))^2-(12*(y-(15/y)))-28 = 0

(y-15*y^-1)^2-12*(y-15*y^-1)-28 = 0

(y-15*y^-1)^2-12*(y-15*y^-1)-28 = 0

y^2-12*y+180*y^-1+225*y^-2-30-28 = 0

y^2-12*y+180*y^-1+225*y^-2-58 = 0

y^2-12*y+180*y^-1+225*y^-2-58 = 0

1*y^2-12*y^1+180*y^-1+225*y^-2-58*y^0 = 0

(1*y^4-12*y^3-58*y^2+180*y^1+225*y^0)/(y^2) = 0 // * y^4

y^2*(1*y^4-12*y^3-58*y^2+180*y^1+225*y^0) = 0

y^2

y^4-12*y^3-58*y^2+180*y+225 = 0

{ 1, -1, 3, -3, 5, -5, 9, -9, 15, -15, 25, -25, 45, -45, 75, -75, 225, -225 }

1

y = 1

y^4-12*y^3-58*y^2+180*y+225 = 336

1

-1

y = -1

y^4-12*y^3-58*y^2+180*y+225 = 0

-1

y+1

y^3-13*y^2-45*y+225

y^4-12*y^3-58*y^2+180*y+225

y+1

-y^4-y^3

180*y-13*y^3-58*y^2+225

13*y^3+13*y^2

180*y-45*y^2+225

45*y^2+45*y

225*y+225

-225*y-225

0

y^3-13*y^2-45*y+225 = 0

{ 1, -1, 3, -3, 5, -5, 9, -9, 15, -15, 25, -25, 45, -45, 75, -75, 225, -225 }

1

y = 1

y^3-13*y^2-45*y+225 = 168

1

-1

y = -1

y^3-13*y^2-45*y+225 = 256

-1

3

y = 3

y^3-13*y^2-45*y+225 = 0

3

y-3

y^2-10*y-75

y^3-13*y^2-45*y+225

y-3

3*y^2-y^3

225-10*y^2-45*y

10*y^2-30*y

225-75*y

75*y-225

0

y^2-10*y-75 = 0

DELTA = (-10)^2-(-75*1*4)

DELTA = 400

DELTA > 0

y = (400^(1/2)+10)/(1*2) or y = (10-400^(1/2))/(1*2)

y = 15 or y = -5

y in { -5, 15, -1, 3} 

(y+5)*(y-15)*(y+1)*(y-3) = 0

(y+5)*(y-15)*(y+1)*(y-3) = 0

( y+1 )

y+1 = 0 // - 1

y = -1

( y+5 )

y+5 = 0 // - 5

y = -5

( y-15 )

y-15 = 0 // + 15

y = 15

( y-3 )

y-3 = 0 // + 3

y = 3

y in { -1, -5, 15, 3 }