To solve this quadratic equation, we can first divide the entire equation by 12 to simplify it:

3x^2 + 2x + 1 = 0

Next, we can use the quadratic formula to find the roots of the equation:

x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in the values a = 3, b = 2, and c = 1 into the formula:

x = (-2 ± √(2^2 - 431)) / 2*3
x = (-2 ± √(4 - 12)) / 6
x = (-2 ± √(-8)) / 6
x = (-2 ± 2i√2) / 6

Therefore, the solutions to the equation are:

x = (-2 + 2i√2) / 6
x = (-2 - 2i√2) / 6

or in simplified form:

x = (-1 ± i√2) / 3