x*(x*0.1)=20000

Solution for x*(x*0.1)=20000 equation:

x(x*0.1)=20000

We move all terms to the left:

x(x*0.1)-(20000)=0

We add all the numbers together, and all the variables

x(+x*0.1)-20000=0

We multiply parentheses

0.1x^2-20000=0

a = 0.1; b = 0; c = -20000;
Δ = b2-4ac
Δ = 02-4·0.1·(-20000)
Δ = 8000
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:

$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{5}}{2*0.1}=\frac{0-40\sqrt{5}}{0.2}
=-\frac{40\sqrt{5}}{0.2}
=-\frac{\sqrt{5}}{0.005}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{5}}{2*0.1}=\frac{0+40\sqrt{5}}{0.2}
=\frac{40\sqrt{5}}{0.2}
=\frac{\sqrt{5}}{0.005}
$