308=w^2

Solution for 308=w^2 equation:

308=w^2

We move all terms to the left:

308-(w^2)=0

We add all the numbers together, and all the variables

-1w^2+308=0

a = -1; b = 0; c = +308;
Δ = b2-4ac
Δ = 02-4·(-1)·308
Δ = 1232
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:

$\sqrt{\Delta}=\sqrt{1232}=\sqrt{16*77}=\sqrt{16}*\sqrt{77}=4\sqrt{77}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{77}}{2*-1}=\frac{0-4\sqrt{77}}{-2}
=-\frac{4\sqrt{77}}{-2}
=-\frac{2\sqrt{77}}{-1}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{77}}{2*-1}=\frac{0+4\sqrt{77}}{-2}
=\frac{4\sqrt{77}}{-2}
=\frac{2\sqrt{77}}{-1}
$