1/6x-1/6-1/9x-10/9=-2

Solution for 1/6x-1/6-1/9x-10/9=-2 equation:

1/6x-1/6-1/9x-10/9=-2

We move all terms to the left:

1/6x-1/6-1/9x-10/9-(-2)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

1/6x-1/9x+2-1/6-10/9=0

We calculate fractions


729x/17496x^2+(-216x)/17496x^2+(-729x)/17496x^2+(-2160x)/17496x^2+2=0

We multiply all the terms by the denominator


729x+(-216x)+(-729x)+(-2160x)+2*17496x^2=0

Wy multiply elements

34992x^2+729x+(-216x)+(-729x)+(-2160x)=0

We get rid of parentheses

34992x^2+729x-216x-729x-2160x=0

We add all the numbers together, and all the variables

34992x^2-2376x=0

a = 34992; b = -2376; c = 0;
Δ = b2-4ac
Δ = -23762-4·34992·0
Δ = 5645376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5645376}=2376$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2376)-2376}{2*34992}=\frac{0}{69984}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2376)+2376}{2*34992}=\frac{4752}{69984}
=11/162
$