\(\dfrac{4}{9}-\left(x-\dfrac{1}{2}\right)^2=\dfrac{1}{3}\\ \Rightarrow\left(x-\dfrac{1}{2}\right)^2=\dfrac{1}{9}\\ \Rightarrow\left[{}\begin{matrix}x-\dfrac{1}{2}=\dfrac{1}{3}\\x-\dfrac{1}{2}=-\dfrac{1}{3}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{5}{6}\\x=\dfrac{1}{6}\end{matrix}\right.\)
\(\dfrac{4}{9}-\left(x-\dfrac{1}{2}\right)^2=\dfrac{1}{3}\\ \left(x-\dfrac{1}{2}\right)^2=\dfrac{4}{9}-\dfrac{1}{3}\\\left(x-\dfrac{1}{2}\right)^2=\dfrac{1}{9}\\ \left(x-\dfrac{1}{2}\right)^2=\left(\dfrac{1}{3}\right)^2\\ \Rightarrow\left[{}\begin{matrix}x-\dfrac{1}{2}=\dfrac{1}{3}\\x-\dfrac{1}{2}=-\dfrac{1}{3}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{5}{6}\\x=\dfrac{1}{6}\end{matrix}\right. \)