0=2w^2-2w-64

Solution for 0=2w^2-2w-64 equation:

0=2w^2-2w-64

We move all terms to the left:

0-(2w^2-2w-64)=0

We add all the numbers together, and all the variables

-(2w^2-2w-64)=0

We get rid of parentheses

-2w^2+2w+64=0

a = -2; b = 2; c = +64;
Δ = b2-4ac
Δ = 22-4·(-2)·64
Δ = 516
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{129}}{2*-2}=\frac{-2-2\sqrt{129}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{129}}{2*-2}=\frac{-2+2\sqrt{129}}{-4}
$