3/1x-6=-1/3x+7

Solution for 3/1x-6=-1/3x+7 equation:

3/1x-6=-1/3x+7

We move all terms to the left:

3/1x-6-(-1/3x+7)=0


Domain of the equation: 1x!=0

x∈R



Domain of the equation: 3x+7)!=0

x∈R


We get rid of parentheses

3/1x+1/3x-7-6=0

We calculate fractions


9x/3x^2+x/3x^2-7-6=0

We add all the numbers together, and all the variables

9x/3x^2+x/3x^2-13=0

We multiply all the terms by the denominator


9x+x-13*3x^2=0

We add all the numbers together, and all the variables

10x-13*3x^2=0

Wy multiply elements

-39x^2+10x=0

a = -39; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-39)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-39}=\frac{-20}{-78}
=10/39
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-39}=\frac{0}{-78}
=0
$