154^2=3w^2

Solution for 154^2=3w^2 equation:

154^2=3w^2

We move all terms to the left:

154^2-(3w^2)=0

We add all the numbers together, and all the variables

-3w^2+23716=0

a = -3; b = 0; c = +23716;
Δ = b2-4ac
Δ = 02-4·(-3)·23716
Δ = 284592
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:

$\sqrt{\Delta}=\sqrt{284592}=\sqrt{94864*3}=\sqrt{94864}*\sqrt{3}=308\sqrt{3}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-308\sqrt{3}}{2*-3}=\frac{0-308\sqrt{3}}{-6}
=-\frac{308\sqrt{3}}{-6}
=-\frac{154\sqrt{3}}{-3}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+308\sqrt{3}}{2*-3}=\frac{0+308\sqrt{3}}{-6}
=\frac{308\sqrt{3}}{-6}
=\frac{154\sqrt{3}}{-3}
$