Given the quadratic function, to get the roots we factorize:
3x²-4x-7=0
3x²+3x-7x-7=0
3x(x+1)-7(x+1)=0
(3x-7)(x+1)=0
thus the roots are
x=-1 or x=3/7
thus the sum of the roots will be:
-1+3/7
=-4/7
To compare you should make the down part equal first
27/45 < 30/45
3 yards fabric costs $7.47
1 yard fabric costs $7.47 / 3
2 yard fabric costs $7.47 / 3 * 2
= $4.98
so, the extra fabric will cost $4.98