-9-5/6x=-2/3x+3

Solution for -9-5/6x=-2/3x+3 equation:

-9-5/6x=-2/3x+3

We move all terms to the left:

-9-5/6x-(-2/3x+3)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x+3)!=0

x∈R


We get rid of parentheses

-5/6x+2/3x-3-9=0

We calculate fractions


(-15x)/18x^2+12x/18x^2-3-9=0

We add all the numbers together, and all the variables

(-15x)/18x^2+12x/18x^2-12=0

We multiply all the terms by the denominator


(-15x)+12x-12*18x^2=0

We add all the numbers together, and all the variables

12x+(-15x)-12*18x^2=0

Wy multiply elements

-216x^2+12x+(-15x)=0

We get rid of parentheses

-216x^2+12x-15x=0

We add all the numbers together, and all the variables

-216x^2-3x=0

a = -216; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-216)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-216}=\frac{0}{-432}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-216}=\frac{6}{-432}
=-1/72
$