1/3(-6x-2)=1/9(2x+34)

Solution for 1/3(-6x-2)=1/9(2x+34) equation:

1/3(-6x-2)=1/9(2x+34)

We move all terms to the left:

1/3(-6x-2)-(1/9(2x+34))=0


Domain of the equation: 3(-6x-2)!=0

x∈R



Domain of the equation: 9(2x+34))!=0

x∈R


We calculate fractions


(9x2/(3(-6x-2)*9(2x+34)))+(-3x0/(3(-6x-2)*9(2x+34)))=0


We calculate terms in parentheses: +(9x2/(3(-6x-2)*9(2x+34))), so:

9x2/(3(-6x-2)*9(2x+34))

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: +(-3x0/(3(-6x-2)*9(2x+34))), so:

-3x0/(3(-6x-2)*9(2x+34))

We multiply all the terms by the denominator


-3x0

We add all the numbers together, and all the variables

-3x

Back to the equation:

+(-3x)


We get rid of parentheses

9x^2-3x=0

a = 9; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·9·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*9}=\frac{0}{18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*9}=\frac{6}{18}
=1/3
$