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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(6(x+4)2x), so:

6(x+4)2x

We multiply parentheses

12x^2+48x

Back to the equation:

-(12x^2+48x)


We get rid of parentheses

-12x^2+6x-48x+12=0

We add all the numbers together, and all the variables

-12x^2-42x+12=0

a = -12; b = -42; c = +12;
Δ = b2-4ac
Δ = -422-4·(-12)·12
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{65}}{2*-12}=\frac{42-6\sqrt{65}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{65}}{2*-12}=\frac{42+6\sqrt{65}}{-24}
$