1. **State the problem:** Solve the quadratic equation $$9x^2 + 16 = 24x$$ using the quadratic formula. 2. **Rewrite the equation in standard form:** Move all terms to one side: $$9x^2 - 24x + 16 = 0$$ 3. **Identify coefficients:** Here, $$a = 9$$, $$b = -24$$, and $$c = 16$$. 4. **Recall the quadratic formula:** $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 5. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-24)^2 - 4 \times 9 \times 16 = 576 - 576 = 0$$ 6. **Since the discriminant is zero, there is exactly one real solution:** $$x = \frac{-(-24)}{2 \times 9} = \frac{24}{18} = \frac{4}{3}$$ 7. **Final answer:** $$x = \frac{4}{3}$$