3/4(12x+8)-9=-1/3(27x-21)

Solution for 3/4(12x+8)-9=-1/3(27x-21) equation:

3/4(12x+8)-9=-1/3(27x-21)

We move all terms to the left:

3/4(12x+8)-9-(-1/3(27x-21))=0


Domain of the equation: 4(12x+8)!=0

x∈R



Domain of the equation: 3(27x-21))!=0

x∈R


We calculate fractions


(9x2/(4(12x+8)*3(27x-21)))+(-(-4x1)/(4(12x+8)*3(27x-21)))-9=0


We calculate terms in parentheses: +(9x2/(4(12x+8)*3(27x-21))), so:

9x2/(4(12x+8)*3(27x-21))

We multiply all the terms by the denominator


9x2

We add all the numbers together, and all the variables

9x^2

Back to the equation:

+(9x^2)



We calculate terms in parentheses: +(-(-4x1)/(4(12x+8)*3(27x-21))), so:

-(-4x1)/(4(12x+8)*3(27x-21))

We add all the numbers together, and all the variables

-(-4x)/(4(12x+8)*3(27x-21))

We multiply all the terms by the denominator


-(-4x)

We get rid of parentheses

4x

Back to the equation:

+(4x)


a = 9; b = 4; c = -9;
Δ = b2-4ac
Δ = 42-4·9·(-9)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{85}}{2*9}=\frac{-4-2\sqrt{85}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{85}}{2*9}=\frac{-4+2\sqrt{85}}{18}
$