1 answer
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lets do it by completion of the square:
x^2+3x+9/4=12+9/4
(x+3/2)^2=57/4
x=-3/2+-sqrt 14.25
so it factors, but into irrational numbers.
(x+1.5+sqrt 14.25)(x+1.5-sqrt 14.25)=0
nice, huh?