9w^2=255

Solution for 9w^2=255 equation:

9w^2=255

We move all terms to the left:

9w^2-(255)=0

a = 9; b = 0; c = -255;
Δ = b2-4ac
Δ = 02-4·9·(-255)
Δ = 9180
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:

$\sqrt{\Delta}=\sqrt{9180}=\sqrt{36*255}=\sqrt{36}*\sqrt{255}=6\sqrt{255}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{255}}{2*9}=\frac{0-6\sqrt{255}}{18}
=-\frac{6\sqrt{255}}{18}
=-\frac{\sqrt{255}}{3}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{255}}{2*9}=\frac{0+6\sqrt{255}}{18}
=\frac{6\sqrt{255}}{18}
=\frac{\sqrt{255}}{3}
$