Answer
$$x=-\frac{-23+\sqrt{1821}}{34},\:x=\frac{23+\sqrt{1821}}{34}$$
Work Step by Step
Using the quadratic formula:
$$ x=\frac{-23 \pm \sqrt{23^2-4\left(-17\right)19}}{2\left(-17\right)} \\ x=-\frac{-23+\sqrt{1821}}{34},\:x=\frac{23+\sqrt{1821}}{34}$$