x=(0.1+x)(0.05+x)

Solution for x=(0.1+x)(0.05+x) equation:

x=(0.1+x)(0.05+x)

We move all terms to the left:

x-((0.1+x)(0.05+x))=0

We add all the numbers together, and all the variables

x-((x+0.1)(x+0.05))=0

We multiply parentheses ..

-((+x^2+0.05x+0.1x+0.005))+x=0


We calculate terms in parentheses: -((+x^2+0.05x+0.1x+0.005)), so:

(+x^2+0.05x+0.1x+0.005)

We get rid of parentheses

x^2+0.05x+0.1x+0.005

We add all the numbers together, and all the variables

x^2+0.15x+0.005

Back to the equation:

-(x^2+0.15x+0.005)


We add all the numbers together, and all the variables

x-(x^2+0.15x+0.005)=0

We get rid of parentheses

-x^2+x-0.15x-0.005=0

We add all the numbers together, and all the variables

-1x^2+0.85x-0.005=0

a = -1; b = 0.85; c = -0.005;
Δ = b2-4ac
Δ = 0.852-4·(-1)·(-0.005)
Δ = 0.7025
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{-(0.85)-\sqrt{0.7025}}{2*-1}=\frac{-0.85-\sqrt{0.7025}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.85)+\sqrt{0.7025}}{2*-1}=\frac{-0.85+\sqrt{0.7025}}{-2}
$