2/3(12x-24)-11=-1/4(24x-12)

Solution for 2/3(12x-24)-11=-1/4(24x-12) equation:

2/3(12x-24)-11=-1/4(24x-12)

We move all terms to the left:

2/3(12x-24)-11-(-1/4(24x-12))=0


Domain of the equation: 3(12x-24)!=0

x∈R



Domain of the equation: 4(24x-12))!=0

x∈R


We calculate fractions


(8x2/(3(12x-24)*4(24x-12)))+(-(-3x1)/(3(12x-24)*4(24x-12)))-11=0


We calculate terms in parentheses: +(8x2/(3(12x-24)*4(24x-12))), so:

8x2/(3(12x-24)*4(24x-12))

We multiply all the terms by the denominator


8x2

We add all the numbers together, and all the variables

8x^2

Back to the equation:

+(8x^2)



We calculate terms in parentheses: +(-(-3x1)/(3(12x-24)*4(24x-12))), so:

-(-3x1)/(3(12x-24)*4(24x-12))

We add all the numbers together, and all the variables

-(-3x)/(3(12x-24)*4(24x-12))

We multiply all the terms by the denominator


-(-3x)

We get rid of parentheses

3x

Back to the equation:

+(3x)


a = 8; b = 3; c = -11;
Δ = b2-4ac
Δ = 32-4·8·(-11)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-19}{2*8}=\frac{-22}{16}
=-1+3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+19}{2*8}=\frac{16}{16}
=1
$