Why is the graph of $8x^2+8xy+2y^2+2x+y+5=0$ empty? For the equation
$$8x^2+8xy+2y^2+2x+y+5=0$$
Comparing it with standard equation of conic section we get that
$h^2-ab=0$ and
$$\Delta= \left|\begin{array}{ccc} 
a & h & g \\
h & b & f \\ 
g & f & c \end{array}\right| = 0$$
So as per I know it should represent a pair of straight line which are real and coincident but after plotting it on desmos( an app to plot graphs) it showed nothing. Please help me.

(as Oscar Lanzi started...)
\begin{align}
   2(2x+y)^2 + (2x+y) + 5 &= 0 \\
   16(2x+y)^2 + 8(2x+y) &= -40 \\
   [4(2x+y)+1]^2 &= -39 \\
\end{align}
