To solve the equation 6x^2 + 2x + 7 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this equation, a = 6, b = 2, and c = 7. Plugging in these values, we get:

x = (-2 ± √(2^2 - 467)) / 26
x = (-2 ± √(4 - 168)) / 12
x = (-2 ± √(-164)) / 12
x = (-2 ± 4√41 i) / 12

Therefore, the solutions for the equation 6x^2 + 2x + 7 = 0 are:

x = (-2 + 4√41 i) / 12 and x = (-2 - 4√41 i) / 12