x^2+120x+3456=6912

Solution for x^2+120x+3456=6912 equation:

x^2+120x+3456=6912

We move all terms to the left:

x^2+120x+3456-(6912)=0

We add all the numbers together, and all the variables

x^2+120x-3456=0

a = 1; b = 120; c = -3456;
Δ = b2-4ac
Δ = 1202-4·1·(-3456)
Δ = 28224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28224}=168$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-168}{2*1}=\frac{-288}{2}
=-144
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+168}{2*1}=\frac{48}{2}
=24
$