2x+1/3x-4=12

Solution for 2x+1/3x-4=12 equation:

2x+1/3x-4=12

We move all terms to the left:

2x+1/3x-4-(12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/3x-16=0

We multiply all the terms by the denominator


2x*3x-16*3x+1=0

Wy multiply elements

6x^2-48x+1=0

a = 6; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·6·1
Δ = 2280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2280}=\sqrt{4*570}=\sqrt{4}*\sqrt{570}=2\sqrt{570}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{570}}{2*6}=\frac{48-2\sqrt{570}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{570}}{2*6}=\frac{48+2\sqrt{570}}{12}
$