7/3x-4=6/2x+4

Solution for 7/3x-4=6/2x+4 equation:

7/3x-4=6/2x+4

We move all terms to the left:

7/3x-4-(6/2x+4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+4)!=0

x∈R


We get rid of parentheses

7/3x-6/2x-4-4=0

We calculate fractions


14x/6x^2+(-18x)/6x^2-4-4=0

We add all the numbers together, and all the variables

14x/6x^2+(-18x)/6x^2-8=0

We multiply all the terms by the denominator


14x+(-18x)-8*6x^2=0

Wy multiply elements

-48x^2+14x+(-18x)=0

We get rid of parentheses

-48x^2+14x-18x=0

We add all the numbers together, and all the variables

-48x^2-4x=0

a = -48; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-48)·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*-48}=\frac{0}{-96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-48}=\frac{8}{-96}
=-1/12
$