Find the discriminant, and determine the number of real solutions. then solve 2x^2+3x-9=0

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