What do you think of mine ?

I continue :

$\displaystyle

={\color{red}\left(3x+y-\frac 12\right)^2}+{\color{blue}3y^2-y+\frac 34}

$

$\displaystyle =\left(3x+y-\frac 12\right)^2+(\sqrt{3}\cdot y)^2-2 \cdot (\sqrt{3}\cdot y)\cdot \frac{1}{2 \sqrt{3}} +\frac 34$

$\displaystyle =\left(3x+y-\frac 12\right)^2+(\sqrt{3}\cdot y)^2-2 \cdot (\sqrt{3}\cdot y)\cdot \frac{1}{2 \sqrt{3}}+(\frac{1}{2\sqrt{3}})^2- (\frac{1}{2\sqrt{3}})^2+\frac 34$

$\displaystyle =\left(3x+y-\frac 12\right)^2+\left(\sqrt{3}\cdot y-\frac{1}{2 \sqrt{3}} \right)^2-\frac{1}{12}+\frac 34$

$\displaystyle =\left(3x+y-\frac 12\right)^2+\left(\sqrt{3}\cdot y-\frac{1}{2 \sqrt{3}} \right)^2+\frac{8}{12}$