.041666666=x+x^2

Solution for .041666666=x+x^2 equation:

.041666666=x+x^2

We move all terms to the left:

.041666666-(x+x^2)=0

We add all the numbers together, and all the variables

-(x+x^2)+0.041666666=0

We get rid of parentheses

-x^2-x+0.041666666=0

We add all the numbers together, and all the variables

-1x^2-1x+0.041666666=0

a = -1; b = -1; c = +0.041666666;
Δ = b2-4ac
Δ = -12-4·(-1)·0.041666666
Δ = 1.166666664
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{1.166666664}}{2*-1}=\frac{1-\sqrt{1.166666664}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1.166666664}}{2*-1}=\frac{1+\sqrt{1.166666664}}{-2}
$