1. **State the problem:** We need to find the discriminant and the number of real solutions for the quadratic equation $$3x^2 - 7x + 1 = 0$$. 2. **Recall the formula for the discriminant:** For a quadratic equation $$ax^2 + bx + c = 0$$, the discriminant $$\Delta$$ is given by: $$\Delta = b^2 - 4ac$$ 3. **Identify coefficients:** Here, $$a = 3$$, $$b = -7$$, and $$c = 1$$. 4. **Calculate the discriminant:** $$\Delta = (-7)^2 - 4 \times 3 \times 1 = 49 - 12 = 37$$ 5. **Interpret the discriminant:** Since $$\Delta = 37 > 0$$, the quadratic equation has two distinct real solutions. **Final answers:** - Discriminant: $$37$$ - Number of real solutions: $$2$$