Discriminant =
b² - 4ac
3² - 4(2)(- 9)
9 + 72
81
Your equation has two real solutions.
2x² + 3x - 9 = 0
2x² + 6x - 3x - 9 = 0
2x(x + 3) - 3(x + 3) = 0
(2x - 3)(x + 3) = 0
Set each equal to zero:
2x - 3 = 0
2x = 3
x = 3/2
x + 3 = 0
x = - 3
Your two solutions are x = - 3, 3/2