2w^2=272

Solution for 2w^2=272 equation:

2w^2=272

We move all terms to the left:

2w^2-(272)=0

a = 2; b = 0; c = -272;
Δ = b2-4ac
Δ = 02-4·2·(-272)
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{34}}{2*2}=\frac{0-8\sqrt{34}}{4}
=-\frac{8\sqrt{34}}{4}
=-2\sqrt{34}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{34}}{2*2}=\frac{0+8\sqrt{34}}{4}
=\frac{8\sqrt{34}}{4}
=2\sqrt{34}
$