1. **State the problem:** Solve the quadratic equation $$80x^{2} + 9x + 30 = 0$$. 2. **Formula used:** The quadratic formula for solving $$ax^{2} + bx + c = 0$$ is $$x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$$. 3. **Identify coefficients:** Here, $$a = 80$$, $$b = 9$$, and $$c = 30$$. 4. **Calculate the discriminant:** $$\Delta = b^{2} - 4ac = 9^{2} - 4 \times 80 \times 30 = 81 - 9600 = -9519$$. 5. Since $$\Delta < 0$$, there are no real solutions; the solutions are complex. 6. **Find the complex solutions:** $$x = \frac{-9 \pm \sqrt{-9519}}{2 \times 80} = \frac{-9 \pm i\sqrt{9519}}{160}$$. 7. **Simplify the square root if possible:** Factor 9519: $$9519 = 9 \times 1057$$, so $$\sqrt{9519} = \sqrt{9 \times 1057} = 3\sqrt{1057}$$. 8. **Final solutions:** $$x = \frac{-9 \pm 3i\sqrt{1057}}{160}$$. This means the two complex roots are $$x = \frac{-9}{160} + \frac{3i\sqrt{1057}}{160}$$ and $$x = \frac{-9}{160} - \frac{3i\sqrt{1057}}{160}$$.