3/4(28x+32)-6=-1/3(24x-24)

Solution for 3/4(28x+32)-6=-1/3(24x-24) equation:

3/4(28x+32)-6=-1/3(24x-24)

We move all terms to the left:

3/4(28x+32)-6-(-1/3(24x-24))=0


Domain of the equation: 4(28x+32)!=0

x∈R



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

x∈R


We calculate fractions


(9x2/(4(28x+32)*3(24x-24)))+(-(-4x2)/(4(28x+32)*3(24x-24)))-6=0


We calculate terms in parentheses: +(9x2/(4(28x+32)*3(24x-24))), so:

9x2/(4(28x+32)*3(24x-24))

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: +(-(-4x2)/(4(28x+32)*3(24x-24))), so:

-(-4x2)/(4(28x+32)*3(24x-24))

We add all the numbers together, and all the variables

-(-4x^2)/(4(28x+32)*3(24x-24))

We multiply all the terms by the denominator


-(-4x^2)

We get rid of parentheses

4x^2

Back to the equation:

+(4x^2)


We add all the numbers together, and all the variables

13x^2-6=0

a = 13; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·13·(-6)
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{78}}{2*13}=\frac{0-2\sqrt{78}}{26}
=-\frac{2\sqrt{78}}{26}
=-\frac{\sqrt{78}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{78}}{2*13}=\frac{0+2\sqrt{78}}{26}
=\frac{2\sqrt{78}}{26}
=\frac{\sqrt{78}}{13}
$