How many solutions does the following equation have?

2x^2 - 3x + 5

(I was going to say just one, I don't know if that's correct or not.)

All quadratic equations have 2 roots; they can be 2 real, different ones, or 2 real, identical ones, or 2 imaginary ones or 2 complex ones. You can tell immediatey from the discriminant b^2-4a (c):

If the D is +, you'll have 2 real, unequal roots;

If 0, you'll have 2 real, equal roots;

If the D is -, you'll have 2 complex or imaginary roots, different

Here a=2, b = - 3 and c = 5, so the discrim. is (-3) ^2 - 4 (2) (5) = 9-40 = - 36.

Because the discrim. is -, you'll have 2 complex roots.