[x2+y2+4x+2y-20=0 needs to be rewritten by completing the squares:
(x2+4x+4)-4+(y2+2y+1)-1-20=0,
(x+2)2+(y+1)2=25, which is a circle centre (-2,-1) radius 5.]
To find the x-intercepts, set y=0 and solve for x:
x2+4x=20, x2+4x+4=24, (x+2)2=24, x+2=±√24=±2√6, so x-intercepts are -2±2√6.
These are points (-2-2√6,0) and (-2+√6,0)=(-6.8990,0) and (2.8990,0) approx.
To find the y-intercepts, set x=0 and solve for y:
y2+2y=20, y2+2y+1=21, (y+1)2=21, y+1=±√21, so y-intercepts are -1±√21.
These are points (0,-1-√21) and (0,-1+√21,0)=(0,-5.5826) and (0,3.5826).