x^2+12x+5=-9

Solution for x^2+12x+5=-9 equation:

x^2+12x+5=-9

We move all terms to the left:

x^2+12x+5-(-9)=0

We add all the numbers together, and all the variables

x^2+12x+14=0

a = 1; b = 12; c = +14;
Δ = b2-4ac
Δ = 122-4·1·14
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{22}}{2*1}=\frac{-12-2\sqrt{22}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{22}}{2*1}=\frac{-12+2\sqrt{22}}{2}
$