x^2=50000

Solution for x^2=50000 equation:

x^2=50000

We move all terms to the left:

x^2-(50000)=0

a = 1; b = 0; c = -50000;
Δ = b2-4ac
Δ = 02-4·1·(-50000)
Δ = 200000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{200000}=\sqrt{40000*5}=\sqrt{40000}*\sqrt{5}=200\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{5}}{2*1}=\frac{0-200\sqrt{5}}{2}
=-\frac{200\sqrt{5}}{2}
=-100\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{5}}{2*1}=\frac{0+200\sqrt{5}}{2}
=\frac{200\sqrt{5}}{2}
=100\sqrt{5}
$