x^2+24x=256

Solution for x^2+24x=256 equation:

x^2+24x=256

We move all terms to the left:

x^2+24x-(256)=0

a = 1; b = 24; c = -256;
Δ = b2-4ac
Δ = 242-4·1·(-256)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-40}{2*1}=\frac{-64}{2}
=-32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+40}{2*1}=\frac{16}{2}
=8
$