(y^3+5y^2-36y-180)/(4y^2-4y-120)

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Solution for (y^3+5y^2-36y-180)/(4y^2-4y-120) equation:


D( y )

4*y^2-(4*y)-120 = 0

4*y^2-(4*y)-120 = 0

4*y^2-(4*y)-120 = 0

4*y^2-4*y-120 = 0

4*y^2-4*y-120 = 0

DELTA = (-4)^2-(-120*4*4)

DELTA = 1936

DELTA > 0

y = (1936^(1/2)+4)/(2*4) or y = (4-1936^(1/2))/(2*4)

y = 6 or y = -5

y in (-oo:-5) U (-5:6) U (6:+oo)

(y^3+5*y^2-(36*y)-180)/(4*y^2-(4*y)-120) = 0

(y^3+5*y^2-36*y-180)/(4*y^2-4*y-120) = 0

y^3+5*y^2-36*y-180 = 0

y^3+5*y^2-36*y-180

y^2*(y+5)-36*y-180

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

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

4*y^2-4*y-120 = 0

4*(y^2-y-30) = 0

y^2-y-30 = 0

DELTA = (-1)^2-(-30*1*4)

DELTA = 121

DELTA > 0

y = (121^(1/2)+1)/(1*2) or y = (1-121^(1/2))/(1*2)

y = 6 or y = -5

4*(y+5)*(y-6) = 0

((y^2-36)*(y+5))/(4*(y+5)*(y-6)) = 0

( y+5 )

y+5 = 0 // - 5

y = -5

( y^2-36 )

1*y^2 = 36 // : 1

y^2 = 36

y^2 = 36 // ^ 1/2

abs(y) = 6

y = 6 or y = -6

y in { -5}

y in { 6}

y = -6

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