1. **State the problem:** Solve the quadratic equation $$x^2 + 2x - 3 = 0$$. 2. **Recall the quadratic formula:** For any quadratic equation $$ax^2 + bx + c = 0$$, the solutions are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$. 3. **Identify coefficients:** Here, $$a = 1$$, $$b = 2$$, and $$c = -3$$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 2^2 - 4 \times 1 \times (-3) = 4 + 12 = 16$$. 5. **Evaluate the square root of the discriminant:** $$\sqrt{16} = 4$$. 6. **Apply the quadratic formula:** $$x = \frac{-2 \pm 4}{2 \times 1} = \frac{-2 \pm 4}{2}$$. 7. **Find the two solutions:** - For the plus sign: $$x = \frac{-2 + 4}{2} = \frac{2}{2} = 1$$. - For the minus sign: $$x = \frac{-2 - 4}{2} = \frac{-6}{2} = -3$$. 8. **Final answer:** The solutions to the equation are $$x = 1$$ and $$x = -3$$.