4n^2+16n+2=-5

Solution for 4n^2+16n+2=-5 equation:

4n^2+16n+2=-5

We move all terms to the left:

4n^2+16n+2-(-5)=0

We add all the numbers together, and all the variables

4n^2+16n+7=0

a = 4; b = 16; c = +7;
Δ = b2-4ac
Δ = 162-4·4·7
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-12}{2*4}=\frac{-28}{8}
=-3+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+12}{2*4}=\frac{-4}{8}
=-1/2
$