12+3x=1/3x-4

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

12+3x=1/3x-4

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

3x-1/3x+4+12=0

We multiply all the terms by the denominator


3x*3x+4*3x+12*3x-1=0

Wy multiply elements

9x^2+12x+36x-1=0

We add all the numbers together, and all the variables

9x^2+48x-1=0

a = 9; b = 48; c = -1;
Δ = b2-4ac
Δ = 482-4·9·(-1)
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-6\sqrt{65}}{2*9}=\frac{-48-6\sqrt{65}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+6\sqrt{65}}{2*9}=\frac{-48+6\sqrt{65}}{18}
$