n^2+12n+23=3

Solution for n^2+12n+23=3 equation:

n^2+12n+23=3

We move all terms to the left:

n^2+12n+23-(3)=0

We add all the numbers together, and all the variables

n^2+12n+20=0

a = 1; b = 12; c = +20;
Δ = b2-4ac
Δ = 122-4·1·20
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8}{2*1}=\frac{-20}{2}
=-10
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8}{2*1}=\frac{-4}{2}
=-2
$