1. The problem is to solve the equation or system given by "solve all" which is ambiguous, so we interpret it as solving a general algebraic equation. 2. Since no specific equation is provided, let's consider a common example: solve the quadratic equation $$ax^2 + bx + c = 0$$. 3. The formula to solve a 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 $$\Delta > 0$$, two distinct real roots. - If $$\Delta = 0$$, one real root (repeated). - If $$\Delta < 0$$, two complex roots. 5. Example: Solve $$2x^2 - 4x - 6 = 0$$. 6. Calculate discriminant: $$\Delta = (-4)^2 - 4 \times 2 \times (-6) = 16 + 48 = 64$$ 7. Since $$\Delta = 64 > 0$$, two real roots. 8. Calculate roots: $$x = \frac{-(-4) \pm \sqrt{64}}{2 \times 2} = \frac{4 \pm 8}{4}$$ 9. Roots: - $$x_1 = \frac{4 + 8}{4} = \frac{12}{4} = 3$$ - $$x_2 = \frac{4 - 8}{4} = \frac{-4}{4} = -1$$ 10. Final answer: The solutions are $$x = 3$$ and $$x = -1$$.