2x+4=14-(1/3x-4)

Solution for 2x+4=14-(1/3x-4) equation:

2x+4=14-(1/3x-4)

We move all terms to the left:

2x+4-(14-(1/3x-4))=0


Domain of the equation: 3x-4))!=0

x∈R


We multiply all the terms by the denominator


2x*3x+4*3x-4))-(14-(1-4))=0

We add all the numbers together, and all the variables

2x*3x+4*3x-4))-(14-(-3))=0

We add all the numbers together, and all the variables

2x*3x+4*3x=0

Wy multiply elements

6x^2+12x=0

a = 6; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·6·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*6}=\frac{-24}{12}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*6}=\frac{0}{12}
=0
$