You can solve that equation without doing any iteration, Claus. Using the formula
your equation is equivalent to
.008*cos(3.14*y/d)^2-.5*cos(3.14*y/d)+.456-x = 0
and this is a quadratic equation in cos(3.14*y/d) which you can solve for. You will then have the unknown y expressed as d/3.14 times the arccosine of the two possible roots of this quadratic. (I presume 3.14 is your approximation for pi.) Provided either of these roots lie between -1 and +1, this will give you an infinite number of possible real-valued solutions for y.