x*2x=1000^2

Solution for x*2x=1000^2 equation:

x*2x=1000^2

We move all terms to the left:

x*2x-(1000^2)=0

We add all the numbers together, and all the variables

x*2x-1000000=0

Wy multiply elements

2x^2-1000000=0

a = 2; b = 0; c = -1000000;
Δ = b2-4ac
Δ = 02-4·2·(-1000000)
Δ = 8000000
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:

$\sqrt{\Delta}=\sqrt{8000000}=\sqrt{4000000*2}=\sqrt{4000000}*\sqrt{2}=2000\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2000\sqrt{2}}{2*2}=\frac{0-2000\sqrt{2}}{4}
=-\frac{2000\sqrt{2}}{4}
=-500\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2000\sqrt{2}}{2*2}=\frac{0+2000\sqrt{2}}{4}
=\frac{2000\sqrt{2}}{4}
=500\sqrt{2}
$