The pairs correspond to the roots of the equations.
I factored all the equations and placed the roots next to each one. Here you have the equations matched with their corresponding roots.
x^2 - 5x - 6 = 0 = (x-6)(x+1) => roots x=6, x=-1
x^2 - 5x + 6 = 0 = (x-3)(x-2) => roots x =2, x=3
3x^2 - 2x - 8 = 0 = (x-2)(3x+4) => roots x = 2, x = -4/3
2x^2 + 9x + 10 = 0 = (x+2)(2x+5) => roots x = -2, x = -5/2
4x^2 + 12x - 7 = 0 = (2x-1)(2x+7) => roots x = 1/2, x = -7/2)
6x^2 - x - 2 = 0 = (2x+1)(3x-2) => roots x =-1/2, x = 2/3
12x^2 - 7x + 1 = 0
=(3x-1)(4x-1) => roots x = 1/3, x = 1/4
