Question 111414
Your work so far is good!
Looking at your quadratic equation:{{{2x^2-102x-59899 = 0}}}, I don't think that you can factor it so you have to use the quadratic formula to solve:
{{{x = (-b+-sqrt(b^2-4ac))/2a}}}
It looks quite formidable with the numbers you have, but it's easy enough with a good calculator. 
{{{x = (-(-102)+-sqrt((-102)2-4(2)(-59899)))/2(2)}}} and you'll get:
{{{x = 200.43}}}
{{{x = -149.43}}}
Take only the positive answer since lengths cannot be negative.
The length (x) is 200.43 feet.
The width (x-51) is 149.43 feet.