2x(x+16)=16

Solution for 2x(x+16)=16 equation:

2x(x+16)=16

We move all terms to the left:

2x(x+16)-(16)=0

We multiply parentheses

2x^2+32x-16=0

a = 2; b = 32; c = -16;
Δ = b2-4ac
Δ = 322-4·2·(-16)
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-24\sqrt{2}}{2*2}=\frac{-32-24\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+24\sqrt{2}}{2*2}=\frac{-32+24\sqrt{2}}{4}
$