Answer
$\begin{align*}
\text{Discriminant: }&
169
\\\text{Number of Real Solutions: }&
2
\end{align*}$
Work Step by Step
In the given equation,
\begin{align*}
2x^2+7x-15=0
,\end{align*} $a=
2
,$ $b=
7
,$ and $c=
-15
.$ Using the Discriminant Formula which is given by $b^2-4ac,$ the value of the discriminant is
\begin{array}{l}\require{cancel}
&
7^2-4(2)(-15)
\\&=
49+120
\\&=
169
\end{array}
Since the discriminant is greater than $0,$ then there are $2$ real solutions.
Hence,
\begin{align*}
\text{Discriminant: }&
169
\\\text{Number of Real Solutions: }&
2
\end{align*}
