Answer
\begin{align*}
\text{Discriminant: }&
1
\\\text{Number of Real Solutions: }&
2
\end{align*}
Work Step by Step
Using the properties of equality, the given equation, $
-2x^2+7x=6
,$ is equivalent to
\begin{align*}
-2x^2+7x-6=0
.\end{align*}
In the equation above $a=
-2
,$ $b=
7
,$ and $c=
-6
.$
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)(-6)
\\&=
49-48
\\&=
1
\end{array}
Since the discriminant is greater than $0,$ then there are $2$ real solutions. Hence,
\begin{align*}
\text{Discriminant: }&
1
\\\text{Number of Real Solutions: }&
2
\end{align*}
