1. **State the problem:** Solve the quadratic equation $2x^2 - 12x - 16 = 0$. 2. **Formula and rules:** The quadratic formula to solve $ax^2 + bx + c = 0$ is: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=2$, $b=-12$, and $c=-16$. 3. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-12)^2 - 4 \times 2 \times (-16) = 144 + 128 = 272$$ 4. **Apply the quadratic formula:** $$x = \frac{-(-12) \pm \sqrt{272}}{2 \times 2} = \frac{12 \pm \sqrt{272}}{4}$$ 5. **Simplify the square root:** $$\sqrt{272} = \sqrt{16 \times 17} = 4\sqrt{17}$$ 6. **Final solutions:** $$x = \frac{12 \pm 4\sqrt{17}}{4} = 3 \pm \sqrt{17}$$ **Answer:** The solutions are $x = 3 + \sqrt{17}$ and $x = 3 - \sqrt{17}$.