Finding a value based on the roots of an equation

Question

So I saw this question recently:

Known $a^2+b^2+6a-12b+45=0$. Find $\dfrac{b-a}{b+a}$.

I tried to factorize it but I don't really know how. Can someone help me with this?

Answer 1

$$ (a+3)^2 + (b-6)^2 = 0 $$ only at $a=-3, b=6$.

Answer 2

HINT :

$$(a^2+6a+9)-9+(b^2-12b+36)-36+45=0$$