x^2=692000000

Solution for x^2=692000000 equation:

x^2=692000000

We move all terms to the left:

x^2-(692000000)=0

a = 1; b = 0; c = -692000000;
Δ = b2-4ac
Δ = 02-4·1·(-692000000)
Δ = 2768000000
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:

$\sqrt{\Delta}=\sqrt{2768000000}=\sqrt{16000000*173}=\sqrt{16000000}*\sqrt{173}=4000\sqrt{173}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4000\sqrt{173}}{2*1}=\frac{0-4000\sqrt{173}}{2}
=-\frac{4000\sqrt{173}}{2}
=-2000\sqrt{173}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4000\sqrt{173}}{2*1}=\frac{0+4000\sqrt{173}}{2}
=\frac{4000\sqrt{173}}{2}
=2000\sqrt{173}
$