3(2x+4)=2x(x+12)

Solution for 3(2x+4)=2x(x+12) equation:

3(2x+4)=2x(x+12)

We move all terms to the left:

3(2x+4)-(2x(x+12))=0

We multiply parentheses

6x-(2x(x+12))+12=0


We calculate terms in parentheses: -(2x(x+12)), so:

2x(x+12)

We multiply parentheses

2x^2+24x

Back to the equation:

-(2x^2+24x)


We get rid of parentheses

-2x^2+6x-24x+12=0

We add all the numbers together, and all the variables

-2x^2-18x+12=0

a = -2; b = -18; c = +12;
Δ = b2-4ac
Δ = -182-4·(-2)·12
Δ = 420
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{105}}{2*-2}=\frac{18-2\sqrt{105}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{105}}{2*-2}=\frac{18+2\sqrt{105}}{-4}
$