Final answer:
After rearranging the equation 5x - 10 = 4x² into the standard quadratic form and calculating the discriminant, which is negative, it can be concluded that the equation has two complex solutions.
Step-by-step explanation:
To use the discriminant to describe the solution(s) of the equation 5x - 10 = 4x², we must first rearrange the equation into the standard quadratic form, which is ax² + bx + c = 0. Doing so, we obtain the equation -4x² + 5x - 10 = 0. The discriminant is given by the formula b² - 4ac, where a, b, and c are the coefficients of the quadratic equation.
In our case, a = -4, b = 5, and c = -10. Plugging these into the discriminant formula, we get:
Discriminant = (5)² - 4(-4)(-10) = 25 - 160 = -135
Since the discriminant is negative (less than 0), this indicates that there are two complex solutions to the quadratic equation.
Therefore, the correct answer is C) Two complex solutions.