0.1x=0.2(x+2)x

Solution for 0.1x=0.2(x+2)x equation:

0.1x=0.2(x+2)x

We move all terms to the left:

0.1x-(0.2(x+2)x)=0


We calculate terms in parentheses: -(0.2(x+2)x), so:

0.2(x+2)x

We multiply parentheses

0x^2+0x

We add all the numbers together, and all the variables

x^2+x

Back to the equation:

-(x^2+x)


We get rid of parentheses

-x^2+0.1x-x=0

We add all the numbers together, and all the variables

-1x^2-0.9x=0

a = -1; b = -0.9; c = 0;
Δ = b2-4ac
Δ = -0.92-4·(-1)·0
Δ = 0.81
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{-(-0.9)-\sqrt{0.81}}{2*-1}=\frac{0.9-\sqrt{0.81}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.9)+\sqrt{0.81}}{2*-1}=\frac{0.9+\sqrt{0.81}}{-2}
$