Let's solve the first equation:
4x^2 + x + 3 = 0

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a

where a = 4, b = 1, and c = 3

x = (-1 ± √(1^2 - 443)) / 2*4
x = (-1 ± √(1 - 48)) / 8
x = (-1 ± √(-47)) / 8
x = (-1 ± √47i) / 8

Therefore, the solutions for the first equation are:
x = (-1 + √47i) / 8 and x = (-1 - √47i) / 8

Now let's solve the second equation:
8x^2 + x + 1 = 0

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a

where a = 8, b = 1, and c = 1

x = (-1 ± √(1^2 - 481)) / 2*8
x = (-1 ± √(1 - 32)) / 16
x = (-1 ± √(-31)) / 16
x = (-1 ± √31i) / 16

Therefore, the solutions for the second equation are:
x = (-1 + √31i) / 16 and x = (-1 - √31i) / 16