The equation of the circle has form:
(x-a)2+(y-b)2=R2, where point (a,b) is the center of the circle, R is its radius.
In your case,
2x2-3x+2y2+4y-20=0 Divide both sides by 2 to get:
x2-3/2*x+y2+2y-10=0; Let us work on y-coordinate of the center first.
y2+2y-10=y2+2y+1-11=(y2+2y+1)-11=(y+1)2-11. Now we made y-part in the form (y-b)2, here b=-1.
Back to the x-part;
Move -9/16 and -11 to the right side to get:
(x2-2*3x/4+9/16)+(y+1)2=11+9/16; ⇔ (x-3/4)2+(y+1)2=185/16;
This is now a canonical form of the equation of a circle. Its center is at the point (3/4;-1)