.0055=x(.20+x)

Solution for .0055=x(.20+x) equation:

.0055=x(.20+x)

We move all terms to the left:

.0055-(x(.20+x))=0

We add all the numbers together, and all the variables

-(x(x+0.2))+.0055=0

We add all the numbers together, and all the variables

-(x(x+0.2))+0.0055=0


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

x(x+0.2)

We multiply parentheses

x^2+0.2x

Back to the equation:

-(x^2+0.2x)


We get rid of parentheses

-x^2-0.2x+0.0055=0

We add all the numbers together, and all the variables

-1x^2-0.2x+0.0055=0

a = -1; b = -0.2; c = +0.0055;
Δ = b2-4ac
Δ = -0.22-4·(-1)·0.0055
Δ = 0.062
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{-(-0.2)-\sqrt{0.062}}{2*-1}=\frac{0.2-\sqrt{0.062}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.2)+\sqrt{0.062}}{2*-1}=\frac{0.2+\sqrt{0.062}}{-2}
$