2/3x+1=9-1/6x

Solution for 2/3x+1=9-1/6x equation:

2/3x+1=9-1/6x

We move all terms to the left:

2/3x+1-(9-1/6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(-1/6x+9)+1=0

We get rid of parentheses

2/3x+1/6x-9+1=0

We calculate fractions


12x/18x^2+3x/18x^2-9+1=0

We add all the numbers together, and all the variables

12x/18x^2+3x/18x^2-8=0

We multiply all the terms by the denominator


12x+3x-8*18x^2=0

We add all the numbers together, and all the variables

15x-8*18x^2=0

Wy multiply elements

-144x^2+15x=0

a = -144; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-144)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-144}=\frac{-30}{-288}
=5/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-144}=\frac{0}{-288}
=0
$