1. **State the problem:** Find the discriminant of the quadratic equation $$-x^2 + 3x - 1 = 0$$. 2. **Recall the formula:** The discriminant $$\Delta$$ of a quadratic equation $$ax^2 + bx + c = 0$$ is given by $$\Delta = b^2 - 4ac$$. 3. **Identify coefficients:** Here, $$a = -1$$, $$b = 3$$, and $$c = -1$$. 4. **Calculate the discriminant:** $$\Delta = 3^2 - 4 \times (-1) \times (-1)$$ $$\Delta = 9 - 4 \times 1$$ $$\Delta = 9 - 4$$ $$\Delta = 5$$ 5. **Interpretation:** Since the discriminant is positive, the quadratic has two distinct real roots. **Final answer:** $$5$$