110=x(.1x)

Solution for 110=x(.1x) equation:

110=x(.1x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(x(+.1x))+110=0


We calculate terms in parentheses: -(x(+.1x)), so:

x(+.1x)

We multiply parentheses

x^2

Back to the equation:

-(x^2)


We add all the numbers together, and all the variables

-1x^2+110=0

a = -1; b = 0; c = +110;
Δ = b2-4ac
Δ = 02-4·(-1)·110
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{110}}{2*-1}=\frac{0-2\sqrt{110}}{-2}
=-\frac{2\sqrt{110}}{-2}
=-\frac{\sqrt{110}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{110}}{2*-1}=\frac{0+2\sqrt{110}}{-2}
=\frac{2\sqrt{110}}{-2}
=\frac{\sqrt{110}}{-1}
$