x^2=300000

Solution for x^2=300000 equation:

x^2=300000

We move all terms to the left:

x^2-(300000)=0

a = 1; b = 0; c = -300000;
Δ = b2-4ac
Δ = 02-4·1·(-300000)
Δ = 1200000
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:

$\sqrt{\Delta}=\sqrt{1200000}=\sqrt{40000*30}=\sqrt{40000}*\sqrt{30}=200\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{30}}{2*1}=\frac{0-200\sqrt{30}}{2}
=-\frac{200\sqrt{30}}{2}
=-100\sqrt{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{30}}{2*1}=\frac{0+200\sqrt{30}}{2}
=\frac{200\sqrt{30}}{2}
=100\sqrt{30}
$