1/2(12x+4)-4=-1/3(21x-6)

Solution for 1/2(12x+4)-4=-1/3(21x-6) equation:

1/2(12x+4)-4=-1/3(21x-6)

We move all terms to the left:

1/2(12x+4)-4-(-1/3(21x-6))=0


Domain of the equation: 2(12x+4)!=0

x∈R



Domain of the equation: 3(21x-6))!=0

x∈R


We calculate fractions


(3x2/(2(12x+4)*3(21x-6)))+(-(-2x1)/(2(12x+4)*3(21x-6)))-4=0


We calculate terms in parentheses: +(3x2/(2(12x+4)*3(21x-6))), so:

3x2/(2(12x+4)*3(21x-6))

We multiply all the terms by the denominator


3x2

We add all the numbers together, and all the variables

3x^2

Back to the equation:

+(3x^2)



We calculate terms in parentheses: +(-(-2x1)/(2(12x+4)*3(21x-6))), so:

-(-2x1)/(2(12x+4)*3(21x-6))

We add all the numbers together, and all the variables

-(-2x)/(2(12x+4)*3(21x-6))

We multiply all the terms by the denominator


-(-2x)

We get rid of parentheses

2x

Back to the equation:

+(2x)


a = 3; b = 2; c = -4;
Δ = b2-4ac
Δ = 22-4·3·(-4)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{13}}{2*3}=\frac{-2-2\sqrt{13}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{13}}{2*3}=\frac{-2+2\sqrt{13}}{6}
$