Answer
discriminant: -92
number of solution: Choice D
Work Step by Step
In the form $ax^2+bx+c=0,$ the given equation, $
4x^2=6x-8
,$ is equivalent to
\begin{align*}
4x^2-6x+8&=0
.\end{align*}
The equation above has
\begin{align*}a=
4
,b=
-6
,\text{ and }c=
8
.\end{align*}
Using $
b^2-4ac
$ or the discriminant, then
\begin{align*}
b^2-4ac&\Rightarrow
(-6)^2-4(4)(8)
\\&=
36-128
\\&=
-92
.\end{align*}
Since the discriminant is $
-92
$ (which is a negative number), then the solutions of $
4x^2=6x-8
$ are two nonreal complex numbers (Choice D).
