x^2=650000

Solution for x^2=650000 equation:

x^2=650000

We move all terms to the left:

x^2-(650000)=0

a = 1; b = 0; c = -650000;
Δ = b2-4ac
Δ = 02-4·1·(-650000)
Δ = 2600000
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:

$\sqrt{\Delta}=\sqrt{2600000}=\sqrt{40000*65}=\sqrt{40000}*\sqrt{65}=200\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{65}}{2*1}=\frac{0-200\sqrt{65}}{2}
=-\frac{200\sqrt{65}}{2}
=-100\sqrt{65}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{65}}{2*1}=\frac{0+200\sqrt{65}}{2}
=\frac{200\sqrt{65}}{2}
=100\sqrt{65}
$