Answer
two real solutions
Work Step by Step
Using the properties of equality, the given quadratic equation, $
8x=3-9x^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
9x^2+8x-3=0
.\end{array}
The quadratic equation above has the following coefficients:
\begin{array}{l}\require{cancel}
a=
9
\\b=
8
\\c=
-3
.\end{array}
Substituting these values into $b^2-4ac$ (or the Discriminant), then the value of the discriminant is
\begin{array}{l}\require{cancel}
(8)^2-4(9)(-3)
\\\\=
64+108
\\\\=
172
.\end{array}
Since the value of the discriminant is $\text{
greater than zero
,}$ then the given quadratic equation has $\text{
two real solutions
}$.
