2n^2+12n+13=3

Solution for 2n^2+12n+13=3 equation:

2n^2+12n+13=3

We move all terms to the left:

2n^2+12n+13-(3)=0

We add all the numbers together, and all the variables

2n^2+12n+10=0

a = 2; b = 12; c = +10;
Δ = b2-4ac
Δ = 122-4·2·10
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*2}=\frac{-20}{4}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8}{2*2}=\frac{-4}{4}
=-1
$