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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-2x^2+8x-(-8x+24)=0

We get rid of parentheses

-2x^2+8x+8x-24=0

We add all the numbers together, and all the variables

-2x^2+16x-24=0

a = -2; b = 16; c = -24;
Δ = b2-4ac
Δ = 162-4·(-2)·(-24)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8}{2*-2}=\frac{-24}{-4}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8}{2*-2}=\frac{-8}{-4}
=+2
$