O.1x=0.2x(x+2)

Solution for O.1x=0.2x(x+2) equation:

.1O=0.2O(O+2)

We move all terms to the left:

.1O-(0.2O(O+2))=0


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

0.2O(O+2)

We multiply parentheses

0O^2+0O

We add all the numbers together, and all the variables

O^2+O

Back to the equation:

-(O^2+O)


We get rid of parentheses

-O^2+.1O-O=0

We add all the numbers together, and all the variables

-1O^2-0.9O=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:
$O_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$O_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$O_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.9)-\sqrt{0.81}}{2*-1}=\frac{0.9-\sqrt{0.81}}{-2}
$
$O_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.9)+\sqrt{0.81}}{2*-1}=\frac{0.9+\sqrt{0.81}}{-2}
$