(y^2)+(5y)=36/(y^2+5y)

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Solution for (y^2)+(5y)=36/(y^2+5y) equation: 


D( y )

y^2+5*y = 0

y^2+5*y = 0

y^2+5*y = 0

y^2+5*y = 0

DELTA = 5^2-(0*1*4)

DELTA = 25

DELTA > 0

y = (25^(1/2)-5)/(1*2) or y = (-25^(1/2)-5)/(1*2)

y = 0 or y = -5

y in (-oo:-5) U (-5:0) U (0:+oo)

y^2+5*y = 36/(y^2+5*y) // - 36/(y^2+5*y)

y^2-(36/(y^2+5*y))+5*y = 0

y^2-36*(y^2+5*y)^-1+5*y = 0

y^2-36/(y^2+5*y)+5*y = 0

y^2+5*y = 0

y^2+5*y = 0

y*(y+5) = 0

y+5 = 0 // - 5

y = -5

y*(y+5) = 0

y^2-36/(y*(y+5))+5*y = 0

(y*y^2*(y+5))/(y*(y+5))-36/(y*(y+5))+(5*y*y*(y+5))/(y*(y+5)) = 0

y*y^2*(y+5)+5*y*y*(y+5)-36 = 0

y^4+5*y^3+5*y^3+25*y^2-36 = 0

y^4+10*y^3+25*y^2-36 = 0

y^4+10*y^3+25*y^2-36 = 0

y^4+10*y^3+25*y^2-36 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 9, -9, 12, -12, 18, -18, 36, -36 }

1

y = 1

y^4+10*y^3+25*y^2-36 = 0

1

y-1

y^3+11*y^2+36*y+36

y^4+10*y^3+25*y^2-36

y-1

y^3-y^4

11*y^3+25*y^2-36

11*y^2-11*y^3

36*y^2-36

36*y-36*y^2

36*y-36

36-36*y

0

y^3+11*y^2+36*y+36 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 9, -9, 12, -12, 18, -18, 36, -36 }

1

y = 1

y^3+11*y^2+36*y+36 = 84

1

-1

y = -1

y^3+11*y^2+36*y+36 = 10

-1

2

y = 2

y^3+11*y^2+36*y+36 = 160

2

-2

y = -2

y^3+11*y^2+36*y+36 = 0

-2

y+2

y^2+9*y+18

y^3+11*y^2+36*y+36

y+2

-y^3-2*y^2

9*y^2+36*y+36

-9*y^2-18*y

18*y+36

-18*y-36

0

y^2+9*y+18 = 0

DELTA = 9^2-(1*4*18)

DELTA = 9

DELTA > 0

y = (9^(1/2)-9)/(1*2) or y = (-9^(1/2)-9)/(1*2)

y = -3 or y = -6

y in { -6, -3, 1, -2} 

(y+6)*(y+3)*(y-1)*(y+2) = 0

((y+6)*(y+3)*(y-1)*(y+2))/(y*(y+5)) = 0

((y+6)*(y+3)*(y-1)*(y+2))/(y*(y+5)) = 0 // * y*(y+5)

(y+6)*(y+3)*(y-1)*(y+2) = 0

( y+2 )

y+2 = 0 // - 2

y = -2

( y+3 )

y+3 = 0 // - 3

y = -3

( y+6 )

y+6 = 0 // - 6

y = -6

( y-1 )

y-1 = 0 // + 1

y = 1

y in { -2, -3, -6, 1 }

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