How many real number solutions are there to the equation 0 equals negative 3X squared plus X -4

To find the number of real number solutions to the equation 0 = -3x^2 + x - 4, we can use the discriminant of the quadratic equation. The discriminant is given by the formula b^2 - 4ac, where the quadratic equation is of the form ax^2 + bx + c = 0.

In this case, a = -3, b = 1, and c = -4. Plugging these values into the discriminant formula, we get:

b^2 - 4ac = 1^2 - 4(-3)(-4)
= 1 - 48
= -47

Since the discriminant is negative (-47), the quadratic equation does not have any real number solutions.