0=2w^2+11-68

Solution for 0=2w^2+11-68 equation:

0=2w^2+11-68

We move all terms to the left:

0-(2w^2+11-68)=0

We add all the numbers together, and all the variables

-(2w^2+11-68)=0

We get rid of parentheses

-2w^2-11+68=0

We add all the numbers together, and all the variables

-2w^2+57=0

a = -2; b = 0; c = +57;
Δ = b2-4ac
Δ = 02-4·(-2)·57
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{114}}{2*-2}=\frac{0-2\sqrt{114}}{-4}
=-\frac{2\sqrt{114}}{-4}
=-\frac{\sqrt{114}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{114}}{2*-2}=\frac{0+2\sqrt{114}}{-4}
=\frac{2\sqrt{114}}{-4}
=\frac{\sqrt{114}}{-2}
$