2/3x+6=1/3x-13x=

Solution for 2/3x+6=1/3x-13x= equation:

2/3x+6=1/3x-13x=

We move all terms to the left:

2/3x+6-(1/3x-13x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x-13x)!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(-13x+1/3x)+6=0

We get rid of parentheses

2/3x+13x-1/3x+6=0

We multiply all the terms by the denominator


13x*3x+6*3x+2-1=0

We add all the numbers together, and all the variables

13x*3x+6*3x+1=0

Wy multiply elements

39x^2+18x+1=0

a = 39; b = 18; c = +1;
Δ = b2-4ac
Δ = 182-4·39·1
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{42}}{2*39}=\frac{-18-2\sqrt{42}}{78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{42}}{2*39}=\frac{-18+2\sqrt{42}}{78}
$