The goal is to find the roots of the equation. That is, the value of x when y=0:

0 = 2x^2-12x-20 (the first thing we can do is factor out 2.)

0=x^2-6x-10 (We cannot easily factor this with reverse foil, so we need to use the quadratic equation (-b + or - sqrt (b^2-4ac))/2a:

a=1, b=-6, c=-10.

(-(-6) + or - sqrt (-6^2 - 4(1)(-10)))/2(1)=

(6 + or - sqrt (36+40))/2 =

(6 + or - sqrt(76))/2 =

(6 + or - sqrt(4*19))/2 =

(6 + or - 2sqrt(19))/2 =

3 + or - sqrt(19)