[tex]8x^2-2x=1\implies8x^2-2x-1=0\implies x^2-\dfrac14x-\dfrac18=0[/tex]
The sum of the roots is [tex]\dfrac14[/tex]. By the fundamental theorem of algebra, a quadratic polynomial has 2 roots [tex]r_1,r_2[/tex] and can be written as
[tex](x-r_1)(x-r_2)=x^2-(r_1+r_2)x+r_1r_2[/tex]
so the sum of the roots is -1 times the coefficient of the degree 1 term.
