x^2+y^2+3x-2y-1=0 find the standard form

Rewrite as

x^2 + 3x + y^2 - 2y = 1

Complete the square on x and y

x^2 + 3x + 9/4 + y^2 - 2y + 1  =  1  + 9/4  + 1

( x + 3/2)^2  +  ( y - 1)^2  =  2 + 9/4

( x + 3/2)^2  +  ( y - 1)^2  =  8/4 + 9/4

( x + 3/2)^2  +  ( y - 1)^2  =  17/4