12x+6=3x(4x+2)

Solution for 12x+6=3x(4x+2) equation:

12x+6=3x(4x+2)

We move all terms to the left:

12x+6-(3x(4x+2))=0


We calculate terms in parentheses: -(3x(4x+2)), so:

3x(4x+2)

We multiply parentheses

12x^2+6x

Back to the equation:

-(12x^2+6x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -12; b = 6; c = +6;
Δ = b2-4ac
Δ = 62-4·(-12)·6
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18}{2*-12}=\frac{-24}{-24}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18}{2*-12}=\frac{12}{-24}
=-1/2
$