4*n+n^2=192

Solution for 4*n+n^2=192 equation:

4n+n^2=192

We move all terms to the left:

4n+n^2-(192)=0

a = 1; b = 4; c = -192;
Δ = b2-4ac
Δ = 42-4·1·(-192)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-28}{2*1}=\frac{-32}{2}
=-16
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+28}{2*1}=\frac{24}{2}
=12
$