x-0.1*(x^2)=0.9

Solution for x-0.1*(x^2)=0.9 equation:

x-0.1(x^2)=0.9

We move all terms to the left:

x-0.1(x^2)-(0.9)=0

determiningTheFunctionDomain
-0.1x^2+x-(0.9)=0

We add all the numbers together, and all the variables

-0.1x^2+x-0.9=0

a = -0.1; b = 1; c = -0.9;
Δ = b2-4ac
Δ = 12-4·(-0.1)·(-0.9)
Δ = 0.64
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{-(1)-\sqrt{0.64}}{2*-0.1}=\frac{-1-\sqrt{0.64}}{-0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{0.64}}{2*-0.1}=\frac{-1+\sqrt{0.64}}{-0.2}
$