x(x+8)=16

Solution for x(x+8)=16 equation:

x(x+8)=16

We move all terms to the left:

x(x+8)-(16)=0

We multiply parentheses

x^2+8x-16=0

a = 1; b = 8; c = -16;
Δ = b2-4ac
Δ = 82-4·1·(-16)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{2}}{2*1}=\frac{-8-8\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{2}}{2*1}=\frac{-8+8\sqrt{2}}{2}
$