x-x^2=0.05

Solution for x-x^2=0.05 equation:

x-x^2=0.05

We move all terms to the left:

x-x^2-(0.05)=0

We add all the numbers together, and all the variables

-1x^2+x-0.05=0

a = -1; b = 1; c = -0.05;
Δ = b2-4ac
Δ = 12-4·(-1)·(-0.05)
Δ = 0.8
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{0.8}}{2*-1}=\frac{-1-\sqrt{0.8}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{0.8}}{2*-1}=\frac{-1+\sqrt{0.8}}{-2}
$