problem: Solve for $x$, where $x > 0$ and $0 = -9x^2 - 3x + 2.$ Express your answer as a simplified common fraction.
solution: We factor and obtain $-(3x - 1)(3x + 2) = 0.$ Clearly, the only positive solution for $x$ occurs when $3x - 1 = 0,$ giving us $x = \boxed{\dfrac{1}{3}}.$