Answer
one real solution
Work Step by Step
Using the properties of equality, the given quadratic equation, $
9x^2+1=6x
,$ is equivalent to
\begin{array}{l}\require{cancel}
9x^2-6x+1=0
.\end{array}
The quadratic equation above has the following coefficients:
\begin{array}{l}\require{cancel}
a=
9
\\b=
-6
\\c=
1
.\end{array}
Substituting these values into $b^2-4ac$ (or the Discriminant), then the value of the discriminant is
\begin{array}{l}\require{cancel}
(-6)^2-4(9)(1)
\\\\=
36-36
\\\\=
0
.\end{array}
Since the value of the discriminant is $\text{
equal to zero
,}$ then the given quadratic equation has $\text{
one real solution
}$.
