1. **State the problem:** Solve the quadratic equation $$6x^2 - 7x - 5 = 0$$ using the quadratic formula and round the solutions to 2 decimal places. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the solutions are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=6$, $b=-7$, and $c=-5$. 3. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-7)^2 - 4 \times 6 \times (-5) = 49 + 120 = 169$$ Since $\Delta > 0$, there are two real solutions. 4. **Find the square root of the discriminant:** $$\sqrt{169} = 13$$ 5. **Calculate the two solutions:** $$x_1 = \frac{-(-7) + 13}{2 \times 6} = \frac{7 + 13}{12} = \frac{20}{12} = 1.6667 \approx 1.67$$ $$x_2 = \frac{-(-7) - 13}{2 \times 6} = \frac{7 - 13}{12} = \frac{-6}{12} = -0.5$$ 6. **Final answer:** The solutions rounded to two decimal places are $$x = 1.67$$ and $$x = -0.50$$.