x(1-x)+2x-4=8x-24-x

Solution for x(1-x)+2x-4=8x-24-x equation:

x(1-x)+2x-4=8x-24-x

We move all terms to the left:

x(1-x)+2x-4-(8x-24-x)=0

We add all the numbers together, and all the variables

x(-1x+1)+2x-(7x-24)-4=0

We add all the numbers together, and all the variables

2x+x(-1x+1)-(7x-24)-4=0

We multiply parentheses

-1x^2+2x+x-(7x-24)-4=0

We get rid of parentheses

-1x^2+2x+x-7x+24-4=0

We add all the numbers together, and all the variables

-1x^2-4x+20=0

a = -1; b = -4; c = +20;
Δ = b2-4ac
Δ = -42-4·(-1)·20
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{6}}{2*-1}=\frac{4-4\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{6}}{2*-1}=\frac{4+4\sqrt{6}}{-2}
$