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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-12x)/162x^2+(-27x)/162x^2+(-66x)/162x^2-1=0

We multiply all the terms by the denominator


(-12x)+(-27x)+(-66x)-1*162x^2=0

Wy multiply elements

-162x^2+(-12x)+(-27x)+(-66x)=0

We get rid of parentheses

-162x^2-12x-27x-66x=0

We add all the numbers together, and all the variables

-162x^2-105x=0

a = -162; b = -105; c = 0;
Δ = b2-4ac
Δ = -1052-4·(-162)·0
Δ = 11025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11025}=105$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-105}{2*-162}=\frac{0}{-324}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+105}{2*-162}=\frac{210}{-324}
=-35/54
$