Answer
$\text{Discriminant: }
233
\\\text{Number of real solutions: }
2$
Work Step by Step
Using the properties of equality, the given equation, $
7-3x=8x^2
,$ is equivalent to
\begin{align*}
-8x^2-3x+7=0
.\end{align*}
Using $ax^2+bx+c=0,$ the equation above has $a=
-8
,$ $b=
-3
,$ and $c=
7
.$ Using $b^2-4ac$ or the Discriminant, then
\begin{align*}b^2-4ac&=
(-3)^2-4(-8)(7)
\\&=
9+224
\\&=
233
.\end{align*}
Since the discriminant above is greater than $0,$ then there are $2$ real solutions. Hence,
\begin{align*}
\text{Discriminant: }
233
\\\text{Number of real solutions: }
2
.\end{align*}
