It's been a few years since I've had a problem like this, so hopefully I am going about this correctly. Start by dividing the equation through by 16 to get:

y^2 + y = 1/16

Now, we figure that in order to factor the left hand side of the equation we would need something of the form (y + c)^2 with c denoting some constant value.

We would like to choose something along the lines of:

(y+1/2)^2 because when you multiply it out you get:

y^2 + y + 1/4. But since we have this additional 1/4 on the left side of the equation, we must add it to the right side to get the full equation:

y^2 + y + 1/4 = 1/16 + 1/4

This becomes: (y + 1/2)^2 = (1/4) + (1/16)

which becomes: (y + 1/2)^2 = 5/16.

Now take the square root of both sides to yield:

y + 1/2 = +/- sqrt(5)/4

Final step: subtract 1/2 from both sides to solve for y:

y = (+/- sqrt(5)/4) - 1/2

I hope this explanation is useful.