4x=x(3x+12)

Solution for 4x=x(3x+12) equation:

4x=x(3x+12)

We move all terms to the left:

4x-(x(3x+12))=0


We calculate terms in parentheses: -(x(3x+12)), so:

x(3x+12)

We multiply parentheses

3x^2+12x

Back to the equation:

-(3x^2+12x)


We get rid of parentheses

-3x^2+4x-12x=0

We add all the numbers together, and all the variables

-3x^2-8x=0

a = -3; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-3)·0
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{-(-8)-8}{2*-3}=\frac{0}{-6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-3}=\frac{16}{-6}
=-2+2/3
$