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n in (-oo:+oo)
(9/2)*n^2+(9/2)*n+1 = 0
9/2*n^2+9/2*n+1 = 0
DELTA = (9/2)^2-(1*4*9/2)
DELTA = 9/4
DELTA > 0
n = ((9/4)^(1/2)-9/2)/(2*9/2) or n = (-(9/4)^(1/2)-9/2)/(2*9/2)
n = -1/3 or n = -2/3
n in { -2/3, -1/3 }
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