3(2x-1)-3x=3x(12+x)

Solution for 3(2x-1)-3x=3x(12+x) equation:

3(2x-1)-3x=3x(12+x)

We move all terms to the left:

3(2x-1)-3x-(3x(12+x))=0

We add all the numbers together, and all the variables

3(2x-1)-3x-(3x(x+12))=0

We add all the numbers together, and all the variables

-3x+3(2x-1)-(3x(x+12))=0

We multiply parentheses

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


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

3x(x+12)

We multiply parentheses

3x^2+36x

Back to the equation:

-(3x^2+36x)


We add all the numbers together, and all the variables

3x-(3x^2+36x)-3=0

We get rid of parentheses

-3x^2+3x-36x-3=0

We add all the numbers together, and all the variables

-3x^2-33x-3=0

a = -3; b = -33; c = -3;
Δ = b2-4ac
Δ = -332-4·(-3)·(-3)
Δ = 1053
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:

$\sqrt{\Delta}=\sqrt{1053}=\sqrt{81*13}=\sqrt{81}*\sqrt{13}=9\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-9\sqrt{13}}{2*-3}=\frac{33-9\sqrt{13}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+9\sqrt{13}}{2*-3}=\frac{33+9\sqrt{13}}{-6}
$