Area of a rectangle is length times width. Let x = the width of the soccer field. That means the length of the field is x + 70.
Now take the formula for area to get A = x(x + 70)
We know area is 7,800 therefore,
7,800 = x(x + 60)
7,800 = x^2 + 70x
0 = x^2 + 70x - 7800
Factoring gives us
0 = (x + 130)(x - 60)
x = -130 or x = 60
Since we are talking about a length, x = -130 makes no sense, so the dimensions of the field are 60 by 130.