x2=4000

Solution for x2=4000 equation:

x2=4000

We move all terms to the left:

x2-(4000)=0

We add all the numbers together, and all the variables

x^2-4000=0

a = 1; b = 0; c = -4000;
Δ = b2-4ac
Δ = 02-4·1·(-4000)
Δ = 16000
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:

$\sqrt{\Delta}=\sqrt{16000}=\sqrt{1600*10}=\sqrt{1600}*\sqrt{10}=40\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{10}}{2*1}=\frac{0-40\sqrt{10}}{2}
=-\frac{40\sqrt{10}}{2}
=-20\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{10}}{2*1}=\frac{0+40\sqrt{10}}{2}
=\frac{40\sqrt{10}}{2}
=20\sqrt{10}
$