Answer
two real solutions
Work Step by Step
Using the properties of equality, the given quadratic equation, $
9x-2x^2+5=0
,$ is equivalent to
\begin{array}{l}\require{cancel}
-2x^2+9x+5=0
.\end{array}
The quadratic equation above has the following coefficients:
\begin{array}{l}\require{cancel}
a=
-2
\\b=
9
\\c=
5
.\end{array}
Substituting these values into $b^2-4ac$ (or the Discriminant), then the value of the discriminant is
\begin{array}{l}\require{cancel}
(9)^2-4(-2)(5)
\\\\=
81+40
\\\\=
121
.\end{array}
Since the value of the discriminant is $\text{
greater than zero
,}$ then the given quadratic equation has $\text{
two real solutions
}$.
