5a^2+6ab+3b^2-30a-20b+46
=5(a^2+6ab/5+3b^2/5-6a-4b+46/5)
=5(a^2+2*3ab/5+(3b/5)^2-2*3a-2*9b/5+3^2+6b^2/25-2b/5+1/5)
=5(a+3/5b-3)^2+6b^2/5-2b+1
=5(a+3/5b-3)^2+6/5(b^2-5b/3+5/6)
=5(a+3/5b-3)^2+6/5(b^2-2*5b/6+(5/6)^2+5/36)
=5(a+3/5b-3)^2+6/5(b-5/6)^2+1/6