w*w=9232

Solution for w*w=9232 equation:

w*w=9232

We move all terms to the left:

w*w-(9232)=0

Wy multiply elements

w^2-9232=0

a = 1; b = 0; c = -9232;
Δ = b2-4ac
Δ = 02-4·1·(-9232)
Δ = 36928
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:

$\sqrt{\Delta}=\sqrt{36928}=\sqrt{64*577}=\sqrt{64}*\sqrt{577}=8\sqrt{577}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{577}}{2*1}=\frac{0-8\sqrt{577}}{2}
=-\frac{8\sqrt{577}}{2}
=-4\sqrt{577}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{577}}{2*1}=\frac{0+8\sqrt{577}}{2}
=\frac{8\sqrt{577}}{2}
=4\sqrt{577}
$