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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

2x/6x^2+3x/6x^2+10=0

We multiply all the terms by the denominator


2x+3x+10*6x^2=0

We add all the numbers together, and all the variables

5x+10*6x^2=0

Wy multiply elements

60x^2+5x=0

a = 60; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·60·0
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*60}=\frac{-10}{120}
=-1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*60}=\frac{0}{120}
=0
$