Answer
The solution set is $\left\{\frac{2}{3}\right\}$.
Work Step by Step
RECALL:
A quadratic equation of the form $ax^2+bx+c=0$ can be solved using the quadratic formula
$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$
The given quadratic equation has:
$a=9
\\b=-12
\\c=4$
Substitute these values into the quadratic formula to obtain:
$x=\dfrac{-(-12) \pm \sqrt{(-12)^2-4(9)(4)}}{2(9)}
\\x=\dfrac{12 \pm \sqrt{144-144}}{18}
\\x=\dfrac{12\pm \sqrt{0}}{18}
\\x =\dfrac{12}{18}
\\x=\dfrac{2}{3}$
Therefore, the solution set is $\left\{\frac{2}{3}\right\}$.
