Algebra

Combining all like terms and bringing all terms to one side, we get

$4x^2 - 8x + 4y^2 + 14y + 12 =0$. 

Now, completing the square fot both x and y, we get

$\left(x-1\right)^2+\left(y-\left(-\frac{7}{4}\right)\right)^2=\left(\frac{\sqrt{17}}{4}\right)^2$

According to the equation of the circle,

we get $r=\sqrt{\left(\frac{\sqrt{17}}{4}\right)^2}=\sqrt{17}/4$

Thanks! :)