0=8-4x-2x^2

Solution for 0=8-4x-2x^2 equation:

0=8-4x-2x^2

We move all terms to the left:

0-(8-4x-2x^2)=0

We add all the numbers together, and all the variables

-(8-4x-2x^2)=0

We get rid of parentheses

2x^2+4x-8=0

a = 2; b = 4; c = -8;
Δ = b2-4ac
Δ = 42-4·2·(-8)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{5}}{2*2}=\frac{-4-4\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{5}}{2*2}=\frac{-4+4\sqrt{5}}{4}
$