1) To solve the equation 4x^2 - 12x + 9 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 4, b = -12, and c = 9. Plugging these values into the quadratic formula, we get:

x = (-(-12) ± √((-12)^2 - 4(4)(9))) / (2(4))
x = (12 ± √(144 - 144)) / 8
x = (12 ± √0) / 8
x = (12 ± 0) / 8

Since the discriminant (b^2 - 4ac) is equal to 0, there is only one solution for x:

x = 12 / 8
x = 3/2

Therefore, the solution to the equation 4x^2 - 12x + 9 = 0 is x = 3/2.

2) To solve the equation 3x^2 + 5x + 2 = 0, we can again use the quadratic formula. In this case, a = 3, b = 5, and c = 2. Plugging these values into the quadratic formula, we get:

x = (-5 ± √(5^2 - 4(3)(2))) / (2(3))
x = (-5 ± √(25 - 24)) / 6
x = (-5 ± √1) / 6
x = (-5 ± 1) / 6

This gives us two possible solutions:

x = (-5 + 1) / 6
x = -4 / 6
x = -2/3

x = (-5 - 1) / 6
x = -6 / 6
x = -1

Therefore, the solutions to the equation 3x^2 + 5x + 2 = 0 are x = -2/3 and x = -1.