Geometry

The formula of a circle is in the form of

$\left(x−a\right)^2+\left(y−b\right)^2=r^2$ where (a,b) is the center and r is the radius. 

First, let's move all the terms to one side. We get

$4x^2-8x+4y^2+14y-12=0$

Dividing everything by 4, we have

$x^2-2x+y^2+7/2y-3=0$

Completing the square for both x and y, we have

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

Thus, the radius is just 

$\sqrt{17}/4$

Thanks! :)