The given quadratic equation is $x^{2}+3 x+9=0$

On comparing the given equation with $a x^{2}+b x+c=0$

We obtain $a=1, b=3,$ and $c=9$

Therefore, the discriminant of the given equation is

$D=b^{2}-4 a c=3^{2}-4 \times 1 \times 9=9-36=-27$

Therefore, the required solutions are

$\frac{-b \pm \sqrt{D}}{2 a}=\frac{-3 \pm \sqrt{-27}}{2(1)}=\frac{-3 \pm 3 \sqrt{-3}}{2}=\frac{-3 \pm 3 \sqrt{3} i}{2} \quad[\sqrt{-1}=i]$