x(x(x(x)))=8000

Solution for x(x(x(x)))=8000 equation:

x(x(x(x)))=8000

We move all terms to the left:

x(x(x(x)))-(8000)=0

determiningTheFunctionDomain
x(xxx)-8000=0

We add all the numbers together, and all the variables

x(+xxx)-8000=0

We multiply parentheses

x^2-8000=0

a = 1; b = 0; c = -8000;
Δ = b2-4ac
Δ = 02-4·1·(-8000)
Δ = 32000
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:

$\sqrt{\Delta}=\sqrt{32000}=\sqrt{6400*5}=\sqrt{6400}*\sqrt{5}=80\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{5}}{2*1}=\frac{0-80\sqrt{5}}{2}
=-\frac{80\sqrt{5}}{2}
=-40\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{5}}{2*1}=\frac{0+80\sqrt{5}}{2}
=\frac{80\sqrt{5}}{2}
=40\sqrt{5}
$