1. **State the problem:** Solve the quadratic equation $$-x^2 + 7x - 18 = 0$$. 2. **Identify coefficients:** Here, $$a = -1$$, $$b = 7$$, and $$c = -18$$. 3. **Recall the quadratic formula:** $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ This formula gives the solutions to any quadratic equation $$ax^2 + bx + c = 0$$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 7^2 - 4(-1)(-18) = 49 - 72 = -23$$ 5. **Interpret the discriminant:** Since $$\Delta < 0$$, there are no real solutions to the equation because the square root of a negative number is not real. 6. **Conclusion:** The quadratic equation $$-x^2 + 7x - 18 = 0$$ has no real solutions.