.667=2x-x^2

Solution for .667=2x-x^2 equation:

.667=2x-x^2

We move all terms to the left:

.667-(2x-x^2)=0

We add all the numbers together, and all the variables

-(2x-x^2)+0.667=0

We get rid of parentheses

x^2-2x+0.667=0

a = 1; b = -2; c = +0.667;
Δ = b2-4ac
Δ = -22-4·1·0.667
Δ = 1.332
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{-(-2)-\sqrt{1.332}}{2*1}=\frac{2-\sqrt{1.332}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{1.332}}{2*1}=\frac{2+\sqrt{1.332}}{2}
$