1/4(24x+24)-3=-1/3(27x-21)

Solution for 1/4(24x+24)-3=-1/3(27x-21) equation:

1/4(24x+24)-3=-1/3(27x-21)

We move all terms to the left:

1/4(24x+24)-3-(-1/3(27x-21))=0


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

x∈R



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

x∈R


We calculate fractions


(3x2/(4(24x+24)*3(27x-21)))+(-(-4x2)/(4(24x+24)*3(27x-21)))-3=0


We calculate terms in parentheses: +(3x2/(4(24x+24)*3(27x-21))), so:

3x2/(4(24x+24)*3(27x-21))

We multiply all the terms by the denominator


3x2

We add all the numbers together, and all the variables

3x^2

Back to the equation:

+(3x^2)



We calculate terms in parentheses: +(-(-4x2)/(4(24x+24)*3(27x-21))), so:

-(-4x2)/(4(24x+24)*3(27x-21))

We add all the numbers together, and all the variables

-(-4x^2)/(4(24x+24)*3(27x-21))

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

7x^2-3=0

a = 7; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·7·(-3)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*7}=\frac{0-2\sqrt{21}}{14}
=-\frac{2\sqrt{21}}{14}
=-\frac{\sqrt{21}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*7}=\frac{0+2\sqrt{21}}{14}
=\frac{2\sqrt{21}}{14}
=\frac{\sqrt{21}}{7}
$