x^2=10^9

Solution for x^2=10^9 equation:

x^2=10^9

We move all terms to the left:

x^2-(10^9)=0

We add all the numbers together, and all the variables

x^2-1000000000=0

a = 1; b = 0; c = -1000000000;
Δ = b2-4ac
Δ = 02-4·1·(-1000000000)
Δ = 4000000000
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:

$\sqrt{\Delta}=\sqrt{4000000000}=\sqrt{400000000*10}=\sqrt{400000000}*\sqrt{10}=20000\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20000\sqrt{10}}{2*1}=\frac{0-20000\sqrt{10}}{2}
=-\frac{20000\sqrt{10}}{2}
=-10000\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20000\sqrt{10}}{2*1}=\frac{0+20000\sqrt{10}}{2}
=\frac{20000\sqrt{10}}{2}
=10000\sqrt{10}
$