1. **State the problem:** We are given the quadratic equation $$25x^2 + 9 = 30x$$ and asked to compute its discriminant and identify the type of solutions. 2. **Rewrite the equation in standard form:** Move all terms to one side: $$25x^2 - 30x + 9 = 0$$ 3. **Identify coefficients:** For a quadratic equation $$ax^2 + bx + c = 0$$, here: $$a = 25, \quad b = -30, \quad c = 9$$ 4. **Formula for the discriminant:** $$\Delta = b^2 - 4ac$$ 5. **Calculate the discriminant:** $$\Delta = (-30)^2 - 4 \times 25 \times 9 = 900 - 900 = 0$$ 6. **Interpret the discriminant:** - If $$\Delta > 0$$, two distinct real solutions. - If $$\Delta = 0$$, one real repeated solution. - If $$\Delta < 0$$, two complex solutions. Since $$\Delta = 0$$, the equation has exactly one real repeated solution (a double root). **Final answer:** The discriminant is $$0$$, so the quadratic equation has one real repeated solution.