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

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

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

We move all terms to the left:

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

We multiply parentheses

12x-(4(x+12)6x)+36=0


We calculate terms in parentheses: -(4(x+12)6x), so:

4(x+12)6x

We multiply parentheses

24x^2+288x

Back to the equation:

-(24x^2+288x)


We get rid of parentheses

-24x^2+12x-288x+36=0

We add all the numbers together, and all the variables

-24x^2-276x+36=0

a = -24; b = -276; c = +36;
Δ = b2-4ac
Δ = -2762-4·(-24)·36
Δ = 79632
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:

$\sqrt{\Delta}=\sqrt{79632}=\sqrt{144*553}=\sqrt{144}*\sqrt{553}=12\sqrt{553}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-276)-12\sqrt{553}}{2*-24}=\frac{276-12\sqrt{553}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-276)+12\sqrt{553}}{2*-24}=\frac{276+12\sqrt{553}}{-48}
$