First, we move all terms to one side to get $ 2x^2 - 4x - 9 = 0 $. Seeing that factoring will not work, we apply the Quadratic Formula: \begin{align*} x &= \frac{-(-4) \pm \sqrt{(-4)^2 - 4(2)(-9)}}{2 (2)}\\ &= \frac{4 \pm \sqrt{16 + 72}}{4} = \frac{4 \pm \sqrt{88}}{4}\\ &= \frac{4 \pm 2\sqrt{22}}{4} = \frac{2 \pm \sqrt{22}}{2}.\end{align*} Since $ x $ is positive, $ x $ can be written as $ \dfrac{2 + \sqrt{22}}{2}, $ so our answer is $ 2 + 22 + 2 = \boxed{26} $.