z^2+12z+9=0

Solution for z^2+12z+9=0 equation:

z^2+12z+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:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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