x^2+0.1x=9*10^-7

Solution for x^2+0.1x=9*10^-7 equation:

x^2+0.1x=9*10^-7

We move all terms to the left:

x^2+0.1x-(9*10^-7)=0

We add all the numbers together, and all the variables

x^2+0.1x-7-9.0E=0

We add all the numbers together, and all the variables

x^2+0.1x-31.4645364561=0

a = 1; b = 0.1; c = -31.4645364561;
Δ = b2-4ac
Δ = 0.12-4·1·(-31.4645364561)
Δ = 125.868145824
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{125.868145824}}{2*1}=\frac{-0.1-\sqrt{125.868145824}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.1)+\sqrt{125.868145824}}{2*1}=\frac{-0.1+\sqrt{125.868145824}}{2}
$