X(x+8)=384

Solution for X(x+8)=384 equation:

X(X+8)=384

We move all terms to the left:

X(X+8)-(384)=0

We multiply parentheses

X^2+8X-384=0

a = 1; b = 8; c = -384;
Δ = b2-4ac
Δ = 82-4·1·(-384)
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{-(8)-40}{2*1}=\frac{-48}{2}
=-24
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+40}{2*1}=\frac{32}{2}
=16
$