x(.1x)=110000

Solution for x(.1x)=110000 equation:

x(.1x)=110000

We move all terms to the left:

x(.1x)-(110000)=0

We add all the numbers together, and all the variables

x(+.1x)-110000=0

We multiply parentheses

x^2-110000=0

a = 1; b = 0; c = -110000;
Δ = b2-4ac
Δ = 02-4·1·(-110000)
Δ = 440000
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:

$\sqrt{\Delta}=\sqrt{440000}=\sqrt{40000*11}=\sqrt{40000}*\sqrt{11}=200\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{11}}{2*1}=\frac{0-200\sqrt{11}}{2}
=-\frac{200\sqrt{11}}{2}
=-100\sqrt{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{11}}{2*1}=\frac{0+200\sqrt{11}}{2}
=\frac{200\sqrt{11}}{2}
=100\sqrt{11}
$