2(x^2+4x-508)=0

Solution for 2(x^2+4x-508)=0 equation:

2(x^2+4x-508)=0

We multiply parentheses

2x^2+8x-1016=0

a = 2; b = 8; c = -1016;
Δ = b2-4ac
Δ = 82-4·2·(-1016)
Δ = 8192
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:

$\sqrt{\Delta}=\sqrt{8192}=\sqrt{4096*2}=\sqrt{4096}*\sqrt{2}=64\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-64\sqrt{2}}{2*2}=\frac{-8-64\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+64\sqrt{2}}{2*2}=\frac{-8+64\sqrt{2}}{4}
$