1. Stating the problem: Solve the quadratic equation $$3x^2 - 4x - 4 = 0$$. 2. Formula used: For a quadratic equation $$ax^2 + bx + c = 0$$, the solutions are given by the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 3. Identify coefficients: Here, $$a = 3$$, $$b = -4$$, and $$c = -4$$. 4. Calculate the discriminant: $$\Delta = b^2 - 4ac = (-4)^2 - 4 \times 3 \times (-4) = 16 + 48 = 64$$ 5. Since $$\Delta > 0$$, there are two real solutions. 6. Calculate the roots: $$x = \frac{-(-4) \pm \sqrt{64}}{2 \times 3} = \frac{4 \pm 8}{6}$$ 7. Find each root: - $$x_1 = \frac{4 + 8}{6} = \frac{12}{6} = 2$$ - $$x_2 = \frac{4 - 8}{6} = \frac{-4}{6} = -\frac{2}{3}$$ 8. Final answer: The solutions to the equation $$3x^2 - 4x - 4 = 0$$ are $$x = 2$$ and $$x = -\frac{2}{3}$$.