4x^2=4000

Solution for 4x^2=4000 equation:

4x^2=4000

We move all terms to the left:

4x^2-(4000)=0

a = 4; b = 0; c = -4000;
Δ = b2-4ac
Δ = 02-4·4·(-4000)
Δ = 64000
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:

$\sqrt{\Delta}=\sqrt{64000}=\sqrt{6400*10}=\sqrt{6400}*\sqrt{10}=80\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{10}}{2*4}=\frac{0-80\sqrt{10}}{8}
=-\frac{80\sqrt{10}}{8}
=-10\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{10}}{2*4}=\frac{0+80\sqrt{10}}{8}
=\frac{80\sqrt{10}}{8}
=10\sqrt{10}
$