Question:
Solve the equation $2 x^{2}+x+1=0$
Solution:
The given quadratic equation is $2 x^{2}+x+1=0$
On comparing the given equation with $a x^{2}+b x+c=0$, we obtain
$a=2, b=1$, and $c=1$
Therefore, the discriminant of the given equation is
$D=b^{2}-4 a c=1^{2}-4 \times 2 \times 1=1-8=-7$
Therefore, the required solutions are
$\frac{-b \pm \sqrt{D}}{2 a}=\frac{-1 \pm \sqrt{-7}}{2 \times 2}=\frac{-1 \pm \sqrt{7} i}{4}$ $[\sqrt{-1}=i]$