1/2x+8=3-1/3x

Solution for 1/2x+8=3-1/3x equation:

1/2x+8=3-1/3x

We move all terms to the left:

1/2x+8-(3-1/3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-1/3x+3)+8=0

We get rid of parentheses

1/2x+1/3x-3+8=0

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5x+5*6x^2=0

Wy multiply elements

30x^2+5x=0

a = 30; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·30·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*30}=\frac{-10}{60}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*30}=\frac{0}{60}
=0
$