1/2(18x+8)=-2/3(21x-12)

Solution for 1/2(18x+8)=-2/3(21x-12) equation:

1/2(18x+8)=-2/3(21x-12)

We move all terms to the left:

1/2(18x+8)-(-2/3(21x-12))=0


Domain of the equation: 2(18x+8)!=0

x∈R



Domain of the equation: 3(21x-12))!=0

x∈R


We calculate fractions


(3x2/(2(18x+8)*3(21x-12)))+(-(-4x1)/(2(18x+8)*3(21x-12)))=0


We calculate terms in parentheses: +(3x2/(2(18x+8)*3(21x-12))), so:

3x2/(2(18x+8)*3(21x-12))

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: +(-(-4x1)/(2(18x+8)*3(21x-12))), so:

-(-4x1)/(2(18x+8)*3(21x-12))

We add all the numbers together, and all the variables

-(-4x)/(2(18x+8)*3(21x-12))

We multiply all the terms by the denominator


-(-4x)

We get rid of parentheses

4x

Back to the equation:

+(4x)


a = 3; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·3·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*3}=\frac{-8}{6}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*3}=\frac{0}{6}
=0
$