1. The problem is to solve an addmath question, but since no specific question was provided, I will demonstrate solving a common addmath problem: solving a quadratic equation. 2. The general form of a quadratic equation is $$ax^2 + bx + c = 0$$. 3. The formula to find the roots of the quadratic equation is the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 4. Important rules: - The discriminant $$\Delta = b^2 - 4ac$$ determines the nature of the roots. - If $$\Delta > 0$$, there are two distinct real roots. - If $$\Delta = 0$$, there is one real root (a repeated root). - If $$\Delta < 0$$, the roots are complex. 5. Example: Solve $$2x^2 - 4x - 6 = 0$$. 6. Identify coefficients: $$a=2$$, $$b=-4$$, $$c=-6$$. 7. Calculate discriminant: $$\Delta = (-4)^2 - 4 \times 2 \times (-6) = 16 + 48 = 64$$ 8. Since $$\Delta = 64 > 0$$, there are two distinct real roots. 9. Apply quadratic formula: $$x = \frac{-(-4) \pm \sqrt{64}}{2 \times 2} = \frac{4 \pm 8}{4}$$ 10. Calculate roots: - $$x_1 = \frac{4 + 8}{4} = \frac{12}{4} = 3$$ - $$x_2 = \frac{4 - 8}{4} = \frac{-4}{4} = -1$$ 11. Final answer: The roots of the equation $$2x^2 - 4x - 6 = 0$$ are $$x=3$$ and $$x=-1$$.