Answer
$\begin{align*}
\text{Discriminant: }&
-223
\\\text{Number of Real Solutions: }&
0
\end{align*}$
Work Step by Step
In the given equation,
\begin{align*}
-2x^2+x-28=0
,\end{align*} $a=
-2
,$ $b=
1
,$ and $c=
-28
.$ 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(-2)(-28)
\\&=
1-224
\\&=
-223
\end{array}
Since the discriminant is less than $0,$ then there is no real solution.
Hence,
\begin{align*}
\text{Discriminant: }&
-223
\\\text{Number of Real Solutions: }&
0
\end{align*}
