1. Let's solve the quadratic equation $2x^2 - 4x - 6 = 0$ as another example. 2. The general form of a quadratic equation is $ax^2 + bx + c = 0$. 3. We use the quadratic formula to find the roots: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 4. Here, $a=2$, $b=-4$, and $c=-6$. 5. Calculate the discriminant: $$\Delta = b^2 - 4ac = (-4)^2 - 4 \times 2 \times (-6) = 16 + 48 = 64$$ 6. Since $\Delta > 0$, there are two real roots. 7. Substitute values into the quadratic formula: $$x = \frac{-(-4) \pm \sqrt{64}}{2 \times 2} = \frac{4 \pm 8}{4}$$ 8. Calculate each root: $$x_1 = \frac{4 + 8}{4} = \frac{12}{4} = 3$$ $$x_2 = \frac{4 - 8}{4} = \frac{-4}{4} = -1$$ 9. Therefore, the solutions are $x=3$ and $x=-1$. This example shows how to apply the quadratic formula step-by-step to find the roots of a quadratic equation.