Final answer:
The equation 3x² - x + 5 = 0 has zero real solutions.
Step-by-step explanation:
To determine the number of real solutions for the equation 3x² - x + 5 = 0, we can use the discriminant. The discriminant is the part of the quadratic formula that is inside the square root, given by b² - 4ac. If the discriminant is positive, there are two real solutions. If it is zero, there is one real solution. If it is negative, there are no real solutions. In this case, the discriminant is (-1)² - 4(3)(5), which is equal to -59. Since the discriminant is negative, there are no real solutions for the given equation.