4(0.1-x)(0.2-x)=x*x

Solution for 4(0.1-x)(0.2-x)=x*x equation:

4(0.1-x)(0.2-x)=x*x

We move all terms to the left:

4(0.1-x)(0.2-x)-(x*x)=0

We add all the numbers together, and all the variables

4(-1x+0.1)(-1x+0.2)-(+x*x)=0

We get rid of parentheses

4(-1x+0.1)(-1x+0.2)-x*x=0

We multiply parentheses ..

4(+x^2-0.2x-0.1x+0.02)-x*x=0

We multiply parentheses

4x^2+0x+0x-x*x+0.08=0

Wy multiply elements

4x^2-1x^2+0x+0x+0.08=0

We add all the numbers together, and all the variables

3x^2+2x+0.08=0

a = 3; b = 2; c = +0.08;
Δ = b2-4ac
Δ = 22-4·3·0.08
Δ = 3.04
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{-(2)-\sqrt{3.04}}{2*3}=\frac{-2-\sqrt{3.04}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+\sqrt{3.04}}{2*3}=\frac{-2+\sqrt{3.04}}{6}
$