1. **State the problem:** Solve the quadratic equation $$x^2 + 20x - 300 = 0$$. 2. **Formula used:** The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where the equation is in the form $$ax^2 + bx + c = 0$$. 3. **Identify coefficients:** Here, $$a = 1$$, $$b = 20$$, and $$c = -300$$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 20^2 - 4 \times 1 \times (-300) = 400 + 1200 = 1600$$. 5. **Find the square root of the discriminant:** $$\sqrt{1600} = 40$$. 6. **Apply the quadratic formula:** $$x = \frac{-20 \pm 40}{2 \times 1} = \frac{-20 \pm 40}{2}$$. 7. **Calculate the two solutions:** - For the plus sign: $$x = \frac{-20 + 40}{2} = \frac{20}{2} = 10$$. - For the minus sign: $$x = \frac{-20 - 40}{2} = \frac{-60}{2} = -30$$. 8. **Final answer:** The solutions to the equation are $$x = 10$$ and $$x = -30$$.