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

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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 $

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