x=x*x/0.1-x

Solution for x=x*x/0.1-x equation:

x=x*x/0.1-x

We move all terms to the left:

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


Domain of the equation: 0.1-x)!=0

We move all terms containing x to the left, all other terms to the right

-x)!=-0.1

x!=-0.1/1

x!=-0.1

x∈R


We add all the numbers together, and all the variables

x-(-1x+x*x/0.1)=0

We get rid of parentheses

x+1x-x*x/0.1=0

We multiply all the terms by the denominator


x*0.1+1x*0.1-x*x=0

Wy multiply elements

-1x^2+0.1x+0.1x=0

We add all the numbers together, and all the variables

-1x^2+0.2x=0

a = -1; b = 0.2; c = 0;
Δ = b2-4ac
Δ = 0.22-4·(-1)·0
Δ = 0.04
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.2)-\sqrt{0.04}}{2*-1}=\frac{-0.2-\sqrt{0.04}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.2)+\sqrt{0.04}}{2*-1}=\frac{-0.2+\sqrt{0.04}}{-2}
$