How to prove that i don't need to find a discriminant to solve the quadratic y^2+6y+9=0?

Well, it is simple, since we recognize in the given form
of the quadratic a perfect square.

We've had been driven by
the formula:

(a+b)^2 = a^2 + 2ab +
b^2

If we'll put a^2 = y^2 and b^2 = 9 => b=3 and
a=y

2ab = 2*3*y = 6y

y^2+6y+9
= (y+3)^2

We'll solve the
quadratic:

(y+3)^2 =
0

(y+3)(y+3) = 0

We'll put
y+3=0

y=-3

The
solutions of the quadratic are real numbers and they are equal: y1=y2 =
-3.