Answer
two complex but not real solutions.
Work Step by Step
Using the properties of equality, the given quadratic equation, $
6=4x-5x^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
5x^2-4x+6=0
.\end{array}
The quadratic equation above has the following coefficients:
\begin{array}{l}\require{cancel}
a=
5
\\b=
-4
\\c=
6
.\end{array}
Substituting these values into $b^2-4ac$ (or the Discriminant), then the value of the discriminant is
\begin{array}{l}\require{cancel}
(-4)^2-4(5)(6)
\\\\=
16-120
\\\\=
-104
.\end{array}
Since the value of the discriminant is $\text{
less than zero
,}$ then the given quadratic equation has $\text{
two complex but not real solutions
}$.