54=2w^2

Solution for 54=2w^2 equation:

54=2w^2

We move all terms to the left:

54-(2w^2)=0

a = -2; b = 0; c = +54;
Δ = b2-4ac
Δ = 02-4·(-2)·54
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*-2}=\frac{0-12\sqrt{3}}{-4}
=-\frac{12\sqrt{3}}{-4}
=-\frac{3\sqrt{3}}{-1}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*-2}=\frac{0+12\sqrt{3}}{-4}
=\frac{12\sqrt{3}}{-4}
=\frac{3\sqrt{3}}{-1}
$