There are two kinds of intercepts, for x=0 and y=0.
For x=0, you obtain f(0)=0^2+0-20=-20.
For y=0, it is easiest to use vieta's formula. For the two solutions x1 and x2, we know x1+x2=-1 and x1*x2=-20. Thus, x1*(-1-x1)=-20, x1^2+x1=20, and we can see x1=4, x2=-5.
Alternatively, write 0=x^2+x-20 as 0=(x+1/2)^2-20.25, the square root of 20.25 is 4.5, so looking at the positive and negative solution of z^2=20.25 with z=x+1/2, you find that 4 and -5 are the two roots of the original equation.
