1/3x+3=8-1/6x

Solution for 1/3x+3=8-1/6x equation:

1/3x+3=8-1/6x

We move all terms to the left:

1/3x+3-(8-1/6x)=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

1/3x-(-1/6x+8)+3=0

We get rid of parentheses

1/3x+1/6x-8+3=0

We calculate fractions


6x/18x^2+3x/18x^2-8+3=0

We add all the numbers together, and all the variables

6x/18x^2+3x/18x^2-5=0

We multiply all the terms by the denominator


6x+3x-5*18x^2=0

We add all the numbers together, and all the variables

9x-5*18x^2=0

Wy multiply elements

-90x^2+9x=0

a = -90; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-90)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-90}=\frac{-18}{-180}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-90}=\frac{0}{-180}
=0
$