52=w2

Solution for 52=w2 equation:

52=w2

We move all terms to the left:

52-(w2)=0

We add all the numbers together, and all the variables

-1w^2+52=0

a = -1; b = 0; c = +52;
Δ = b2-4ac
Δ = 02-4·(-1)·52
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{13}}{2*-1}=\frac{0-4\sqrt{13}}{-2}
=-\frac{4\sqrt{13}}{-2}
=-\frac{2\sqrt{13}}{-1}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{13}}{2*-1}=\frac{0+4\sqrt{13}}{-2}
=\frac{4\sqrt{13}}{-2}
=\frac{2\sqrt{13}}{-1}
$