Answer
$2\text{ $x$-intercepts}$
Work Step by Step
Using $y=ax^2+bx+c,$ the given equation,
\begin{align*}
y=-5x^2-4x+3
,\end{align*} has $a=
-5
,$ $b=
-4
,$ and $c=
3
.$
Using the Discriminant Formula which is given by $b^2-4ac,$ the value of the discriminant is
\begin{array}{l}\require{cancel}
&
(-4)^2-4(-5)(3)
\\&=
16+60
\\&=
76
\end{array}
Since the discriminant is greater than $0,$ then there are $
2
$ real solutions. With $
2
$ real solutions, then the graph of the given equation has $
2\text{ $x$-intercepts}
.$