5x=3x(4-x)

Solution for 5x=3x(4-x) equation:

5x=3x(4-x)

We move all terms to the left:

5x-(3x(4-x))=0

We add all the numbers together, and all the variables

5x-(3x(-1x+4))=0


We calculate terms in parentheses: -(3x(-1x+4)), so:

3x(-1x+4)

We multiply parentheses

-3x^2+12x

Back to the equation:

-(-3x^2+12x)


We get rid of parentheses

3x^2-12x+5x=0

We add all the numbers together, and all the variables

3x^2-7x=0

a = 3; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·3·0
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{-(-7)-7}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*3}=\frac{14}{6}
=2+1/3
$