1. **Problem:** Find the roots of the quadratic equation $$5 - 5x - 2x^2 = 0$$. 2. **Rewrite the equation in standard form:** $$-2x^2 - 5x + 5 = 0$$ Multiply both sides by $$-1$$ to make the leading coefficient positive: $$\cancel{-2}x^2 + \cancel{5}x - \cancel{5} = 0 \Rightarrow 2x^2 + 5x - 5 = 0$$ 3. **Use the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the roots are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ Here, $$a = 2$$, $$b = 5$$, and $$c = -5$$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 5^2 - 4 \times 2 \times (-5) = 25 + 40 = 65$$ 5. **Find the roots:** $$x = \frac{-5 \pm \sqrt{65}}{2 \times 2} = \frac{-5 \pm \sqrt{65}}{4}$$ 6. **Final answer:** The roots of the equation are $$x = \frac{-5 + \sqrt{65}}{4} \quad \text{and} \quad x = \frac{-5 - \sqrt{65}}{4}$$