Recall the quadratic formula to solve for \(x\): \(x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\), where \(a\), \(b\), and \(c\) are coefficients from the equation \(ax^{2} + bx + c = 0\).
Substitute the values from the equation into the formula: \(a = 1\), \(b = 9\), and \(c = -22\).
Use the discriminant to find the two possible solutions for \(x\) by evaluating \(x = \frac{-9 \pm \sqrt{\Delta}}{2}\), then select the positive solution.