1/3(21x+6)-18=-1/4(24x-16)

Solution for 1/3(21x+6)-18=-1/4(24x-16) equation:

1/3(21x+6)-18=-1/4(24x-16)

We move all terms to the left:

1/3(21x+6)-18-(-1/4(24x-16))=0


Domain of the equation: 3(21x+6)!=0

x∈R



Domain of the equation: 4(24x-16))!=0

x∈R


We calculate fractions


(4x2/(3(21x+6)*4(24x-16)))+(-(-3x2)/(3(21x+6)*4(24x-16)))-18=0


We calculate terms in parentheses: +(4x2/(3(21x+6)*4(24x-16))), so:

4x2/(3(21x+6)*4(24x-16))

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(21x+6)*4(24x-16))), so:

-(-3x2)/(3(21x+6)*4(24x-16))

We add all the numbers together, and all the variables

-(-3x^2)/(3(21x+6)*4(24x-16))

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^2-18=0

a = 7; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·7·(-18)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{14}}{2*7}=\frac{0-6\sqrt{14}}{14}
=-\frac{6\sqrt{14}}{14}
=-\frac{3\sqrt{14}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{14}}{2*7}=\frac{0+6\sqrt{14}}{14}
=\frac{6\sqrt{14}}{14}
=\frac{3\sqrt{14}}{7}
$