1/3x-6=3/7x+4

Solution for 1/3x-6=3/7x+4 equation:

1/3x-6=3/7x+4

We move all terms to the left:

1/3x-6-(3/7x+4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 7x+4)!=0

x∈R


We get rid of parentheses

1/3x-3/7x-4-6=0

We calculate fractions


7x/21x^2+(-9x)/21x^2-4-6=0

We add all the numbers together, and all the variables

7x/21x^2+(-9x)/21x^2-10=0

We multiply all the terms by the denominator


7x+(-9x)-10*21x^2=0

Wy multiply elements

-210x^2+7x+(-9x)=0

We get rid of parentheses

-210x^2+7x-9x=0

We add all the numbers together, and all the variables

-210x^2-2x=0

a = -210; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-210)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-210}=\frac{0}{-420}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-210}=\frac{4}{-420}
=-1/105
$