Question:
Solve the equation $x^{2}+3 x+9=0$
Solution:
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
$D=b^{2}-4 a c=3^{2}-4 \times 1 \times 9=9-36=-27$
$\frac{-b \pm \sqrt{D}}{2 a}=\frac{-3 \pm \sqrt{-27}}{2(1)}=\frac{-3 \pm 3 \sqrt{-3}}{2}=\frac{-3 \pm 3 \sqrt{3} i}{2}$ $[\sqrt{-1}=i]$