2(4x+6)=(2/3)(12x+18)

Solution for 2(4x+6)=(2/3)(12x+18) equation:

2(4x+6)=(2/3)(12x+18)

We move all terms to the left:

2(4x+6)-((2/3)(12x+18))=0


Domain of the equation: 3)(12x+18))!=0

x∈R


We add all the numbers together, and all the variables

2(4x+6)-((+2/3)(12x+18))=0

We multiply parentheses

8x-((+2/3)(12x+18))+12=0

We multiply parentheses ..

-((+24x^2+2/3*18))+8x+12=0

We multiply all the terms by the denominator


-((+24x^2+2+8x*3*18))+12*3*18))=0


We calculate terms in parentheses: -((+24x^2+2+8x*3*18)), so:

(+24x^2+2+8x*3*18)

We get rid of parentheses

24x^2+8x*3*18+2

Wy multiply elements

24x^2+432x*1+2

Wy multiply elements

24x^2+432x+2

Back to the equation:

-(24x^2+432x+2)


We add all the numbers together, and all the variables

-(24x^2+432x+2)=0

We get rid of parentheses

-24x^2-432x-2=0

a = -24; b = -432; c = -2;
Δ = b2-4ac
Δ = -4322-4·(-24)·(-2)
Δ = 186432
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:

$\sqrt{\Delta}=\sqrt{186432}=\sqrt{64*2913}=\sqrt{64}*\sqrt{2913}=8\sqrt{2913}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-432)-8\sqrt{2913}}{2*-24}=\frac{432-8\sqrt{2913}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-432)+8\sqrt{2913}}{2*-24}=\frac{432+8\sqrt{2913}}{-48}
$