what is the radius?

2 x^2 - 5 x+ 2 y^2 - 3 y = 0

We need to complete the square on x and y

2( x^2 - (5/2)x + 25/16) + 2(y^2 - (3/2)y + 9/16)  =  50/16 + 18/16

2(x - 5/4)^2   + 2 (y - 3/4)^2   =   68/16      

2( x - 5/4)^2   + 2(y - 3/4)^2   =  17/4    divide both sides by 2

(x - 5/4)^2   + (y - 3/4)^2   =  17/8

So...the radius  = √(17/8)  = about 1.458