4x=3x(9-x)

Solution for 4x=3x(9-x) equation:

4x=3x(9-x)

We move all terms to the left:

4x-(3x(9-x))=0

We add all the numbers together, and all the variables

4x-(3x(-1x+9))=0


We calculate terms in parentheses: -(3x(-1x+9)), so:

3x(-1x+9)

We multiply parentheses

-3x^2+27x

Back to the equation:

-(-3x^2+27x)


We get rid of parentheses

3x^2-27x+4x=0

We add all the numbers together, and all the variables

3x^2-23x=0

a = 3; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·3·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*3}=\frac{46}{6}
=7+2/3
$