Answer
Discriminant: $
64
$
Number of Real Solutions: $
2
$
Number of Imaginary Solutions: $
0
$
Work Step by Step
Using $ax^2+bx+c=0,$ the given equation,
\begin{align*}
x^2+6x-7=0
,\end{align*} has $a=
1
,$ $b=
6
,$ and $c=
-7
.$ Using $b^2-4ac$ or the Discriminant, then
\begin{align*}\require{cancel}b^2-4ac&\Rightarrow
6^2-4(1)(-7)
\\&=
36+28
\\&=
64
.\end{align*}
Since the value of the discriminant is greater than $0,$ then there are $2$ real solutions.
