48=w2

Solution for 48=w2 equation:

48=w2

We move all terms to the left:

48-(w2)=0

We add all the numbers together, and all the variables

-1w^2+48=0

a = -1; b = 0; c = +48;
Δ = b2-4ac
Δ = 02-4·(-1)·48
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*-1}=\frac{0-8\sqrt{3}}{-2}
=-\frac{8\sqrt{3}}{-2}
=-\frac{4\sqrt{3}}{-1}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*-1}=\frac{0+8\sqrt{3}}{-2}
=\frac{8\sqrt{3}}{-2}
=\frac{4\sqrt{3}}{-1}
$