6x=3(x+4)x

Solution for 6x=3(x+4)x equation:

6x=3(x+4)x

We move all terms to the left:

6x-(3(x+4)x)=0


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

3(x+4)x

We multiply parentheses

3x^2+12x

Back to the equation:

-(3x^2+12x)


We get rid of parentheses

-3x^2+6x-12x=0

We add all the numbers together, and all the variables

-3x^2-6x=0

a = -3; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-3)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-3}=\frac{0}{-6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-3}=\frac{12}{-6}
=-2
$