-5/6x+2/3x-1/6x=-189

Solution for -5/6x+2/3x-1/6x=-189 equation:

-5/6x+2/3x-1/6x=-189

We move all terms to the left:

-5/6x+2/3x-1/6x-(-189)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-5/6x+2/3x-1/6x+189=0

We calculate fractions


(-3x-5)/18x^2+12x/18x^2+189=0

We multiply all the terms by the denominator


(-3x-5)+12x+189*18x^2=0

We add all the numbers together, and all the variables

12x+(-3x-5)+189*18x^2=0

Wy multiply elements

3402x^2+12x+(-3x-5)=0

We get rid of parentheses

3402x^2+12x-3x-5=0

We add all the numbers together, and all the variables

3402x^2+9x-5=0

a = 3402; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·3402·(-5)
Δ = 68121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{68121}=261$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-261}{2*3402}=\frac{-270}{6804}
=-5/126
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+261}{2*3402}=\frac{252}{6804}
=1/27
$