Question

how many real number equations does this equation have?
0= -7x^2+6x+3
A. 1 solution*
B. 2 solutions
C. no solutions
D. infintie solutions

Answer 1

should be "how many real number equations..."
Recall the determinant: b^2-4ac
If it is zero, there is a single root. Here, the determinant is 6^2+4(-7)(3) = 120
So, your choice is incorrect.
FYI, regarding the determinant:
positive: 2 roots
zero: 1 root
negative: no real roots

This is because in the quadratic formula the roots are

x = (-b±√(b^2-4ac))/2a
so, if the determinant is positive, you are adding/subtracting a real nonzero value from -b/2a
you can see what happens if it is zero or negative.

It's called the discriminant because it discriminates among the kinds of roots.

Answer 2

b² - 4 a c
is the discriminant not determinant.

Answer 3

thanks for the catch. I also failed to correct his "equations" for "solutions"
Must have been a Freudian slip
(that's when you say one thing, but mean your mother)