How many real-number solutions does the equation have?

1. –7x² + 6x + 3 = 0
a. one solution
b. two solutions
c. no solutions
d. infinitely many solutions

2.–8x² – 8x – 2 = 0
a. one solution
b. two solutions
c. no solutions
d. infinitely many solutions

If the discriminant is negative no real solution exists.
If the discriminant is equal to 0 only one real solution exists.
If the discriminant is positive 2 real solutions exist.
The discriminant:
D = b² - 4 a c
1 ) - 7 x² + 6 x + 3 = 0
D = 6² - 4 · ( - 7 ) · 3 = 36 + 84 = 120  > 0
b) two solutions
2 ) - 8 x² - 8 x - 2 = 0
D = ( - 8 )² - 4 · ( - 8 ) · ( - 2 ) = 64 - 64 = 0
a ) one solution