Prove algebraically that the straight line with equation x = 2y + 10 is a tangent to the circle with equation x² + y² = 20

My working:

x=2y+10
x²+y²=20
4y²+40y+100+y²=20
5y²+40y+100=20
5y²+40y+80=0
5(y²+8y+16)=0
y²+8y+16=0
(y+4)²=0
y=-4
x=2y+10
x=-8+10
x=2
x=2, y=-4