2w*w=12500

Solution for 2w*w=12500 equation:

2w*w=12500

We move all terms to the left:

2w*w-(12500)=0

Wy multiply elements

2w^2-12500=0

a = 2; b = 0; c = -12500;
Δ = b2-4ac
Δ = 02-4·2·(-12500)
Δ = 100000
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:

$\sqrt{\Delta}=\sqrt{100000}=\sqrt{10000*10}=\sqrt{10000}*\sqrt{10}=100\sqrt{10}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{10}}{2*2}=\frac{0-100\sqrt{10}}{4}
=-\frac{100\sqrt{10}}{4}
=-25\sqrt{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{10}}{2*2}=\frac{0+100\sqrt{10}}{4}
=\frac{100\sqrt{10}}{4}
=25\sqrt{10}
$