Use the discriminant to determine the number and types of solutions of the quadratic equation. 7=3x-3x^2

First let's rearrange the equation so it's in the form 0 = ax^2 + bx + c:
7 = 3x - 3x^2
0 = -3x^2 + 3x - 7

The discriminant = b^2 - 4ac
Discriminant = (3)^2 - 4(-3)(-7)
= 9 - 84
= -75

Since the discriminant is less than 0 there are no real solutions

(If the discriminant = 0, there is one solution
If the discriminant > 0 and is a perfect square, there are two rational solutions
If the discriminant > 0 and is not a perfect square, there are two irrational solutions)