52/3x+2=11/6x-4

Solution for 52/3x+2=11/6x-4 equation:

52/3x+2=11/6x-4

We move all terms to the left:

52/3x+2-(11/6x-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-11/6x+4+2=0

We calculate fractions


312x/18x^2+(-33x)/18x^2+4+2=0

We add all the numbers together, and all the variables

312x/18x^2+(-33x)/18x^2+6=0

We multiply all the terms by the denominator


312x+(-33x)+6*18x^2=0

Wy multiply elements

108x^2+312x+(-33x)=0

We get rid of parentheses

108x^2+312x-33x=0

We add all the numbers together, and all the variables

108x^2+279x=0

a = 108; b = 279; c = 0;
Δ = b2-4ac
Δ = 2792-4·108·0
Δ = 77841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{77841}=279$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(279)-279}{2*108}=\frac{-558}{216}
=-2+7/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(279)+279}{2*108}=\frac{0}{216}
=0
$