1000^2+x^2=2000^2

Solution for 1000^2+x^2=2000^2 equation:

1000^2+x^2=2000^2

We move all terms to the left:

1000^2+x^2-(2000^2)=0

We add all the numbers together, and all the variables

x^2-3000000=0

a = 1; b = 0; c = -3000000;
Δ = b2-4ac
Δ = 02-4·1·(-3000000)
Δ = 12000000
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:

$\sqrt{\Delta}=\sqrt{12000000}=\sqrt{4000000*3}=\sqrt{4000000}*\sqrt{3}=2000\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2000\sqrt{3}}{2*1}=\frac{0-2000\sqrt{3}}{2}
=-\frac{2000\sqrt{3}}{2}
=-1000\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2000\sqrt{3}}{2*1}=\frac{0+2000\sqrt{3}}{2}
=\frac{2000\sqrt{3}}{2}
=1000\sqrt{3}
$