2(3x+2)=(1/2)(12x+6)

Solution for 2(3x+2)=(1/2)(12x+6) equation:

2(3x+2)=(1/2)(12x+6)

We move all terms to the left:

2(3x+2)-((1/2)(12x+6))=0


Domain of the equation: 2)(12x+6))!=0

x∈R


We add all the numbers together, and all the variables

2(3x+2)-((+1/2)(12x+6))=0

We multiply parentheses

6x-((+1/2)(12x+6))+4=0

We multiply parentheses ..

-((+12x^2+1/2*6))+6x+4=0

We multiply all the terms by the denominator


-((+12x^2+1+6x*2*6))+4*2*6))=0


We calculate terms in parentheses: -((+12x^2+1+6x*2*6)), so:

(+12x^2+1+6x*2*6)

We get rid of parentheses

12x^2+6x*2*6+1

Wy multiply elements

12x^2+72x*6+1

Wy multiply elements

12x^2+432x+1

Back to the equation:

-(12x^2+432x+1)


We add all the numbers together, and all the variables

-(12x^2+432x+1)=0

We get rid of parentheses

-12x^2-432x-1=0

a = -12; b = -432; c = -1;
Δ = b2-4ac
Δ = -4322-4·(-12)·(-1)
Δ = 186576
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:

$\sqrt{\Delta}=\sqrt{186576}=\sqrt{2704*69}=\sqrt{2704}*\sqrt{69}=52\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-432)-52\sqrt{69}}{2*-12}=\frac{432-52\sqrt{69}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-432)+52\sqrt{69}}{2*-12}=\frac{432+52\sqrt{69}}{-24}
$