x^2+6x+9=-6x

Solution for x^2+6x+9=-6x equation:

x^2+6x+9=-6x

We move all terms to the left:

x^2+6x+9-(-6x)=0

We get rid of parentheses

x^2+6x+6x+9=0

We add all the numbers together, and all the variables

x^2+12x+9=0

a = 1; b = 12; c = +9;
Δ = b2-4ac
Δ = 122-4·1·9
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{3}}{2*1}=\frac{-12-6\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{3}}{2*1}=\frac{-12+6\sqrt{3}}{2}
$