Algebra

so, we can simplify the equation to be $4x^2-8x+4y^2+14y=-12.$

dividing the equation by 4, we get $x^2-2x+y^2+7y/2=-3$

completing the square, we get $(x-1)^2+(y+\frac{7}{4})^2=\frac{17}{16}$

17/16 is the radius squared, so we take the square root and get $\boxed{\frac{\sqrt{17}}{4}}$