3(2x-8)=2(4-x)x=

Solution for 3(2x-8)=2(4-x)x= equation:

3(2x-8)=2(4-x)x=

We move all terms to the left:

3(2x-8)-(2(4-x)x)=0

We add all the numbers together, and all the variables

3(2x-8)-(2(-1x+4)x)=0

We multiply parentheses

6x-(2(-1x+4)x)-24=0


We calculate terms in parentheses: -(2(-1x+4)x), so:

2(-1x+4)x

We multiply parentheses

-2x^2+8x

Back to the equation:

-(-2x^2+8x)


We get rid of parentheses

2x^2-8x+6x-24=0

We add all the numbers together, and all the variables

2x^2-2x-24=0

a = 2; b = -2; c = -24;
Δ = b2-4ac
Δ = -22-4·2·(-24)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*2}=\frac{16}{4}
=4
$