x^2=12500

Solution for x^2=12500 equation:

x^2=12500

We move all terms to the left:

x^2-(12500)=0

a = 1; b = 0; c = -12500;
Δ = b2-4ac
Δ = 02-4·1·(-12500)
Δ = 50000
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:

$\sqrt{\Delta}=\sqrt{50000}=\sqrt{10000*5}=\sqrt{10000}*\sqrt{5}=100\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{5}}{2*1}=\frac{0-100\sqrt{5}}{2}
=-\frac{100\sqrt{5}}{2}
=-50\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{5}}{2*1}=\frac{0+100\sqrt{5}}{2}
=\frac{100\sqrt{5}}{2}
=50\sqrt{5}
$