0.001x+x^2-(1*10^-9)=0

Solution for 0.001x+x^2-(1*10^-9)=0 equation:

0.001x+x^2-(1*10^-9)=0

We add all the numbers together, and all the variables

x^2+0.001x-9-1.0E=0

We add all the numbers together, and all the variables

x^2+0.001x-11.718281828459=0

a = 1; b = 0.001; c = -11.718281828459;
Δ = b2-4ac
Δ = 0.0012-4·1·(-11.718281828459)
Δ = 46.873128313836
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{-(0.001)-\sqrt{46.873128313836}}{2*1}=\frac{-0.001-\sqrt{46.873128313836}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.001)+\sqrt{46.873128313836}}{2*1}=\frac{-0.001+\sqrt{46.873128313836}}{2}
$