The focus of the parabola $y=2x^2+x$ is

$y=2x^2+x$

$x^2+\frac{x}{2}=\frac{y}{2}$

${(x+\frac{1}{4})}^2=\frac{1}{2}(y+\frac{1}{8})$

Can be  re  written as

$x^2=\frac{1}{2}y\to \left(1\right)$

$x+\frac{1}{4}=xy+\frac{1}{8}=y$

comparing $x^2=4Ay$

$A=\frac{1}{8}\text{ focus }\left(1\right)\text{ is }(0,1/R)$

$x-0y=\frac{1}{8}$

$x+\frac{1}{4}=0y+\frac{1}{8}=\frac{1}{8}$

$x=\frac{-1}{4}y=0$

$(x,y)=(\frac{-1}{4},0)$