0.000623=(0.1+x)x

Solution for 0.000623=(0.1+x)x equation:

0.000623=(0.1+x)x

We move all terms to the left:

0.000623-((0.1+x)x)=0

We add all the numbers together, and all the variables

-((x+0.1)x)+0.000623=0


We calculate terms in parentheses: -((x+0.1)x), so:

(x+0.1)x

We multiply parentheses

x^2+0.1x

Back to the equation:

-(x^2+0.1x)


We get rid of parentheses

-x^2-0.1x+0.000623=0

We add all the numbers together, and all the variables

-1x^2-0.1x+0.000623=0

a = -1; b = -0.1; c = +0.000623;
Δ = b2-4ac
Δ = -0.12-4·(-1)·0.000623
Δ = 0.012492
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{-(-0.1)-\sqrt{0.012492}}{2*-1}=\frac{0.1-\sqrt{0.012492}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.1)+\sqrt{0.012492}}{2*-1}=\frac{0.1+\sqrt{0.012492}}{-2}
$