1. **State the problem:** Find the discriminant of the quadratic equation and determine how many real solutions it has. 2. **Rewrite the equation:** Given $7 = -9x^2$, rewrite it in standard quadratic form $ax^2 + bx + c = 0$. $$-9x^2 - 7 = 0$$ Here, $a = -9$, $b = 0$, and $c = -7$. 3. **Recall the discriminant formula:** $$\Delta = b^2 - 4ac$$ The discriminant tells us the nature of the roots: - If $\Delta > 0$, two distinct real solutions. - If $\Delta = 0$, one real solution. - If $\Delta < 0$, no real solutions. 4. **Calculate the discriminant:** $$\Delta = 0^2 - 4 \times (-9) \times (-7) = 0 - 4 \times 63 = 0 - 252 = -252$$ 5. **Interpret the result:** Since $\Delta = -252 < 0$, the equation has no real solutions. **Final answer:** The discriminant is $-252$, so there are no real solutions.