8=2x^2-4x-8

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

8=2x^2-4x-8

We move all terms to the left:

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

We get rid of parentheses

-2x^2+4x+8+8=0

We add all the numbers together, and all the variables

-2x^2+4x+16=0

a = -2; b = 4; c = +16;
Δ = b2-4ac
Δ = 42-4·(-2)·16
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12}{2*-2}=\frac{-16}{-4}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12}{2*-2}=\frac{8}{-4}
=-2
$