4n+n^2+7=124

Solution for 4n+n^2+7=124 equation:

4n+n^2+7=124

We move all terms to the left:

4n+n^2+7-(124)=0

We add all the numbers together, and all the variables

n^2+4n-117=0

a = 1; b = 4; c = -117;
Δ = b2-4ac
Δ = 42-4·1·(-117)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-22}{2*1}=\frac{-26}{2}
=-13
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+22}{2*1}=\frac{18}{2}
=9
$