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

Solution for 0=(0.1+x)*(0.05+x) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((+x^2+0.05x+0.1x+0.005))=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 get rid of parentheses

-x^2-0.15x-0.005=0

We add all the numbers together, and all the variables

-1x^2-0.15x-0.005=0

a = -1; b = -0.15; c = -0.005;
Δ = b2-4ac
Δ = -0.152-4·(-1)·(-0.005)
Δ = 0.0025
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{-(-0.15)-\sqrt{0.0025}}{2*-1}=\frac{0.15-\sqrt{0.0025}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.15)+\sqrt{0.0025}}{2*-1}=\frac{0.15+\sqrt{0.0025}}{-2}
$