2/3(12x+27)-16=-1/4(24x-20)

Solution for 2/3(12x+27)-16=-1/4(24x-20) equation:

2/3(12x+27)-16=-1/4(24x-20)

We move all terms to the left:

2/3(12x+27)-16-(-1/4(24x-20))=0


Domain of the equation: 3(12x+27)!=0

x∈R



Domain of the equation: 4(24x-20))!=0

x∈R


We calculate fractions


(8x2/(3(12x+27)*4(24x-20)))+(-(-3x1)/(3(12x+27)*4(24x-20)))-16=0


We calculate terms in parentheses: +(8x2/(3(12x+27)*4(24x-20))), so:

8x2/(3(12x+27)*4(24x-20))

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+27)*4(24x-20))), so:

-(-3x1)/(3(12x+27)*4(24x-20))

We add all the numbers together, and all the variables

-(-3x)/(3(12x+27)*4(24x-20))

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 = -16;
Δ = b2-4ac
Δ = 32-4·8·(-16)
Δ = 521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{521}}{2*8}=\frac{-3-\sqrt{521}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{521}}{2*8}=\frac{-3+\sqrt{521}}{16}
$