1. **State the problem:** Find the discriminant of the quadratic equation and determine how many real solutions it has. The equation is given as: $$1 = -5t^2 - 7t$$ 2. **Rewrite the equation in standard form:** Bring all terms to one side: $$-5t^2 - 7t - 1 = 0$$ 3. **Identify coefficients:** For a quadratic equation $$at^2 + bt + c = 0$$, here: $$a = -5, \quad b = -7, \quad c = -1$$ 4. **Formula for the discriminant:** $$\Delta = b^2 - 4ac$$ 5. **Calculate the discriminant:** $$\Delta = (-7)^2 - 4 \times (-5) \times (-1) = 49 - 20 = 29$$ 6. **Interpret the discriminant:** - If $$\Delta > 0$$, there are two distinct real solutions. - If $$\Delta = 0$$, there is exactly one real solution. - If $$\Delta < 0$$, there are no real solutions. Since $$\Delta = 29 > 0$$, the equation has two real solutions. **Final answer:** The equation has two real solutions.