11/3x-1/6=11/2x+8

Solution for 11/3x-1/6=11/2x+8 equation:

11/3x-1/6=11/2x+8

We move all terms to the left:

11/3x-1/6-(11/2x+8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+8)!=0

x∈R


We get rid of parentheses

11/3x-11/2x-8-1/6=0

We calculate fractions


(-12x^2)/216x^2+792x/216x^2+(-1188x)/216x^2-8=0

We multiply all the terms by the denominator


(-12x^2)+792x+(-1188x)-8*216x^2=0

Wy multiply elements

(-12x^2)-1728x^2+792x+(-1188x)=0

We get rid of parentheses

-12x^2-1728x^2+792x-1188x=0

We add all the numbers together, and all the variables

-1740x^2-396x=0

a = -1740; b = -396; c = 0;
Δ = b2-4ac
Δ = -3962-4·(-1740)·0
Δ = 156816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{156816}=396$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-396)-396}{2*-1740}=\frac{0}{-3480}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-396)+396}{2*-1740}=\frac{792}{-3480}
=-33/145
$