2x*(1-x)=x-6

Solution for 2x*(1-x)=x-6 equation:

2x(1-x)=x-6

We move all terms to the left:

2x(1-x)-(x-6)=0

We add all the numbers together, and all the variables

2x(-1x+1)-(x-6)=0

We multiply parentheses

-2x^2+2x-(x-6)=0

We get rid of parentheses

-2x^2+2x-x+6=0

We add all the numbers together, and all the variables

-2x^2+x+6=0

a = -2; b = 1; c = +6;
Δ = b2-4ac
Δ = 12-4·(-2)·6
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*-2}=\frac{-8}{-4}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*-2}=\frac{6}{-4}
=-1+1/2
$