To solve the quadratic equation 9x^2 - 6x + 2 = 0, we can use the quadratic formula:

x = (-B ± √(B^2 - 4AC)) / 2A

In this equation, A = 9, B = -6, and C = 2.

Plugging these values into the formula:

x = (6 ± √((-6)^2 - 492)) / 2*9
x = (6 ± √(36 - 72)) / 18
x = (6 ± √(-36)) / 18

Since the square root of a negative number is imaginary, the solutions are complex numbers:

x = (6 ± 6i) / 18

Therefore, the solutions to the equation 9x^2 - 6x + 2 = 0 are:

x = (6 + 6i) / 18
x = (6 - 6i) / 18