2z^2+12z+9=0

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

2z^2+12z+9=0

a = 2; b = 12; c = +9;
Δ = b2-4ac
Δ = 122-4·2·9
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{2}}{2*2}=\frac{-12-6\sqrt{2}}{4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{2}}{2*2}=\frac{-12+6\sqrt{2}}{4}
$