0=2x^2+16x-16

Solution for 0=2x^2+16x-16 equation:

0=2x^2+16x-16

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-2x^2-16x+16=0

a = -2; b = -16; c = +16;
Δ = b2-4ac
Δ = -162-4·(-2)·16
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{6}}{2*-2}=\frac{16-8\sqrt{6}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{6}}{2*-2}=\frac{16+8\sqrt{6}}{-4}
$