jmc

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: $$\begin{array}{rl}x& =\frac{-(-4)\pm \sqrt{(-4{)}^2-4(2)(-9)}}{2(2)}\\ & =\frac{4\pm \sqrt{16+72}}{4}=\frac{4\pm \sqrt{88}}{4}\\ & =\frac{4\pm 2\sqrt{22}}{4}=\frac{2\pm \sqrt{22}}{2}.\end{array}$$Since $x$ is positive, $x$ can be written as $\frac{2+\sqrt{22}}{2},$ so our answer is $2+22+2=\boxed{26}.$