For any solution it follows that y=y so:
x^2+2x=3x+20 subtract 3x from both sides
x^2-x=20 subtract 20 from both sides
x^2-x-20=0 factor...
x^2-5x+4x-20=0
x(x-5)+4(x-5)=0
(x+4)(x-5)=0
x=-4 and 5 now to find the corresponding y values I'll use y=x^2+2x
y(-4)=16-8=8 and y(5)=25+10=35 so the two solutions are the points:
(-4, 8) and (5, 35)