4x=3x(8-x)

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

4x=3x(8-x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(3x(-1x+8)), so:

3x(-1x+8)

We multiply parentheses

-3x^2+24x

Back to the equation:

-(-3x^2+24x)


We get rid of parentheses

3x^2-24x+4x=0

We add all the numbers together, and all the variables

3x^2-20x=0

a = 3; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·3·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*3}=\frac{40}{6}
=6+2/3
$