1/3(24x+6)-5=-1/4(28x-24)

Solution for 1/3(24x+6)-5=-1/4(28x-24) equation:

1/3(24x+6)-5=-1/4(28x-24)

We move all terms to the left:

1/3(24x+6)-5-(-1/4(28x-24))=0


Domain of the equation: 3(24x+6)!=0

x∈R



Domain of the equation: 4(28x-24))!=0

x∈R


We calculate fractions


(4x2/(3(24x+6)*4(28x-24)))+(-(-3x2)/(3(24x+6)*4(28x-24)))-5=0


We calculate terms in parentheses: +(4x2/(3(24x+6)*4(28x-24))), so:

4x2/(3(24x+6)*4(28x-24))

We multiply all the terms by the denominator


4x2

We add all the numbers together, and all the variables

4x^2

Back to the equation:

+(4x^2)



We calculate terms in parentheses: +(-(-3x2)/(3(24x+6)*4(28x-24))), so:

-(-3x2)/(3(24x+6)*4(28x-24))

We add all the numbers together, and all the variables

-(-3x^2)/(3(24x+6)*4(28x-24))

We multiply all the terms by the denominator


-(-3x^2)

We get rid of parentheses

3x^2

Back to the equation:

+(3x^2)


We add all the numbers together, and all the variables

7x^2-5=0

a = 7; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·7·(-5)
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{35}}{2*7}=\frac{0-2\sqrt{35}}{14}
=-\frac{2\sqrt{35}}{14}
=-\frac{\sqrt{35}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{35}}{2*7}=\frac{0+2\sqrt{35}}{14}
=\frac{2\sqrt{35}}{14}
=\frac{\sqrt{35}}{7}
$