Final answer:
The given equation 16x² + 24x + 9 = 0 has two real and equal solutions.
Step-by-step explanation:
The given equation is 16x² + 24x + 9 = 0. To determine the nature of the solutions, we can use the discriminant.
The discriminant (D) can be calculated using the formula D = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation.
In this case, a = 16, b = 24, and c = 9.
Substituting these values into the discriminant formula, we have D = (24)² - 4(16)(9) = 576 - 576 = 0.
Since the discriminant is equal to zero, the equation has two real and equal solutions.