To solve each of these quadratic equations, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by x = (-b ± √(b^2 - 4ac)) / 2a.

1) For 2x^2 - 3x - 9 = 0:
a = 2, b = -3, c = -9
x = (-(-3) ± √((-3)^2 - 42(-9))) / 2*2
x = (3 ± √(9 + 72)) / 4
x = (3 ± √81) / 4
x = (3 ± 9) / 4
x = (12) / 4 or x = (-6) / 4
x = 3 or x = -1.5

Therefore, the solutions are x = 3 and x = -1.5.

2) For 5x^2 + 3x + 4 = 0:
a = 5, b = 3, c = 4
x = (-3 ± √(3^2 - 454)) / 2*5
x = (-3 ± √(9 - 80)) / 10
x = (-3 ± √(-71)) / 10
The discriminant is negative, so the solutions are complex numbers. The solutions are x = (-3 ± √71i) / 10.

3) For 3x^2 - 2x - 8 = 0:
a = 3, b = -2, c = -8
x = (2 ± √((-2)^2 - 43(-8))) / 2*3
x = (2 ± √(4 + 96)) / 6
x = (2 ± √100) / 6
x = (2 ± 10) / 6
x = 12 / 6 or x = -8 / 6
x = 2 or x = -4/3

Therefore, the solutions are x = 2 and x = -4/3.