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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(12x(x-3)), so:

12x(x-3)

We multiply parentheses

12x^2-36x

Back to the equation:

-(12x^2-36x)


We get rid of parentheses

-12x^2+6x+36x+6=0

We add all the numbers together, and all the variables

-12x^2+42x+6=0

a = -12; b = 42; c = +6;
Δ = b2-4ac
Δ = 422-4·(-12)·6
Δ = 2052
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:

$\sqrt{\Delta}=\sqrt{2052}=\sqrt{36*57}=\sqrt{36}*\sqrt{57}=6\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{57}}{2*-12}=\frac{-42-6\sqrt{57}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{57}}{2*-12}=\frac{-42+6\sqrt{57}}{-24}
$