Graphically this is a circle and line intersection.
Substitute y=2x-4 in x2+y2=36:
x2+(2x-4)2=36,
x2+4x2-16x+16=36,
5x2-16x-20=0,
x=(16±√(256+400))/10=(16±√656)/10=(8±2√41)/5.
y=2x-4=(-4±4√41)/5.
(x,y)=((8+2√41)/5,(-4+4√41)/5) or ((8-2√41)/5,(-4-4√41)/5);
(x,y)=(4.1612,4.3225) or (-0.9612,-5.9225) approx.