(x)(x+16)=384

Solution for (x)(x+16)=384 equation:

(x)(x+16)=384

We move all terms to the left:

(x)(x+16)-(384)=0

We multiply parentheses

x^2+16x-384=0

a = 1; b = 16; c = -384;
Δ = b2-4ac
Δ = 162-4·1·(-384)
Δ = 1792
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16\sqrt{7}}{2*1}=\frac{-16-16\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16\sqrt{7}}{2*1}=\frac{-16+16\sqrt{7}}{2}
$