52/3x+2=1/6x-4

Solution for 52/3x+2=1/6x-4 equation:

52/3x+2=1/6x-4

We move all terms to the left:

52/3x+2-(1/6x-4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x-4)!=0

x∈R


We get rid of parentheses

52/3x-1/6x+4+2=0

We calculate fractions


312x/18x^2+(-3x)/18x^2+4+2=0

We add all the numbers together, and all the variables

312x/18x^2+(-3x)/18x^2+6=0

We multiply all the terms by the denominator


312x+(-3x)+6*18x^2=0

Wy multiply elements

108x^2+312x+(-3x)=0

We get rid of parentheses

108x^2+312x-3x=0

We add all the numbers together, and all the variables

108x^2+309x=0

a = 108; b = 309; c = 0;
Δ = b2-4ac
Δ = 3092-4·108·0
Δ = 95481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{95481}=309$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(309)-309}{2*108}=\frac{-618}{216}
=-2+31/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(309)+309}{2*108}=\frac{0}{216}
=0
$