Answer
\begin{align*}
\text{Discriminant: }&
-23
\\\text{Number of Real Solutions: }&
0
\end{align*}
Work Step by Step
Using the properties of equality, the given equation, $
x+2=-3x^2
,$ is equivalent to
\begin{align*}
3x^2+x+2=0
\end{align*}
In the equation above $a=
3
,$ $b=
1
,$ and $c=
2
.$
Using the Discriminant Formula which is given by $b^2-4ac,$ the value of the discriminant is
\begin{array}{l}\require{cancel}
&
1^2-4(3)(2)
\\&=
1-24
\\&=
-23
\end{array}
Since the discriminant is less than $0,$ then there is no real solution. Hence,
\begin{align*}
\text{Discriminant: }&
-23
\\\text{Number of Real Solutions: }&
0
\end{align*}
