a^2=25000

Solution for a^2=25000 equation:

a^2=25000

We move all terms to the left:

a^2-(25000)=0

a = 1; b = 0; c = -25000;
Δ = b2-4ac
Δ = 02-4·1·(-25000)
Δ = 100000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{100000}=\sqrt{10000*10}=\sqrt{10000}*\sqrt{10}=100\sqrt{10}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{10}}{2*1}=\frac{0-100\sqrt{10}}{2}
=-\frac{100\sqrt{10}}{2}
=-50\sqrt{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{10}}{2*1}=\frac{0+100\sqrt{10}}{2}
=\frac{100\sqrt{10}}{2}
=50\sqrt{10}
$