6x2-35x-5≡ax2+bx+c; a=6, ac=-30, b=-35, b2=1225, c=-5; 4ac=-120; 2a=12.
To solve the quadratic 6x2-35x-5=0, use the quadratic formula:
x=(-b±√(b2-4ac))/(2a)
x=(35±√(1225+120))/12=(35±√1345)/12=5.97285 or -0.13952 (approx).
These are the zeroes of the quadratic x2-35x/6-⅚, so the original quadratic factorises:
6(x-5.97285)(x+0.13952)=6(x2-35x/6-⅚).
The product of the zeroes using these values is -0.83333 and c/6=-⅚=-0.83333 to the same accuracy.
The sum of the zeros is 5.97285-0.13952=5.83333 and -b/6=35/6=5⅚=5.83333 to the same accuracy.