Answer
Discriminant: 88
Nature of Solutions: two irrational solutions
Work Step by Step
Using $ax^2+bx+c=0$, the given equation $
2x^2-8x-3=0
$ has
\begin{align*}
a=2,b=-8,\text{ and }c=-3
.\end{align*}
Using $
b^2-4ac
$ or the discriminant, then
\begin{align*}
b^2-4ac&\Rightarrow
(-8)^2-4(2)(-3)
\\&=
64+24
\\&=
88
.\end{align*}
Since the discriminat is $88$ (which is a positive and a nonperfect square number), then the equation $2x^2-8x-3=0$ has two irrational solutions.
