4a^2+9b^2-4a+12b+5=0
(4a^2-4a+1)+(9b^2+12b+4)=0
(2a-1)^2+(3b+2)^2=0
(2a-1)^2=0,(3b+2)^2=0
2a-1=0,3b+2=0
a=1/2,b=-2/3