1. **State the problem:** Solve the quadratic equation $$16x^2 - 81 = 0$$. 2. **Formula and rules:** This is a difference of squares problem, which can be factored using the identity $$a^2 - b^2 = (a - b)(a + b)$$. 3. **Factor the equation:** $$16x^2 - 81 = (4x)^2 - 9^2 = (4x - 9)(4x + 9) = 0$$ 4. **Set each factor equal to zero:** $$4x - 9 = 0 \quad \text{or} \quad 4x + 9 = 0$$ 5. **Solve each equation:** $$4x - 9 = 0 \Rightarrow 4x = 9 \Rightarrow x = \frac{9}{4}$$ $$4x + 9 = 0 \Rightarrow 4x = -9 \Rightarrow x = -\frac{9}{4}$$ 6. **Final answer:** $$x = \pm \frac{9}{4}$$ The correct choice is D: $$-\frac{9}{4}, \frac{9}{4}$$.