4(x+3)=(1/3)(12x+9)

Solution for 4(x+3)=(1/3)(12x+9) equation:

4(x+3)=(1/3)(12x+9)

We move all terms to the left:

4(x+3)-((1/3)(12x+9))=0


Domain of the equation: 3)(12x+9))!=0

x∈R


We add all the numbers together, and all the variables

4(x+3)-((+1/3)(12x+9))=0

We multiply parentheses

4x-((+1/3)(12x+9))+12=0

We multiply parentheses ..

-((+12x^2+1/3*9))+4x+12=0

We multiply all the terms by the denominator


-((+12x^2+1+4x*3*9))+12*3*9))=0


We calculate terms in parentheses: -((+12x^2+1+4x*3*9)), so:

(+12x^2+1+4x*3*9)

We get rid of parentheses

12x^2+4x*3*9+1

Wy multiply elements

12x^2+108x*9+1

Wy multiply elements

12x^2+972x+1

Back to the equation:

-(12x^2+972x+1)


We add all the numbers together, and all the variables

-(12x^2+972x+1)=0

We get rid of parentheses

-12x^2-972x-1=0

a = -12; b = -972; c = -1;
Δ = b2-4ac
Δ = -9722-4·(-12)·(-1)
Δ = 944736
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:

$\sqrt{\Delta}=\sqrt{944736}=\sqrt{16*59046}=\sqrt{16}*\sqrt{59046}=4\sqrt{59046}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-972)-4\sqrt{59046}}{2*-12}=\frac{972-4\sqrt{59046}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-972)+4\sqrt{59046}}{2*-12}=\frac{972+4\sqrt{59046}}{-24}
$