1/3x+4=-x-2

Solution for 1/3x+4=-x-2 equation:

1/3x+4=-x-2

We move all terms to the left:

1/3x+4-(-x-2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(-1x-2)+4=0

We get rid of parentheses

1/3x+1x+2+4=0

We multiply all the terms by the denominator


1x*3x+2*3x+4*3x+1=0

Wy multiply elements

3x^2+6x+12x+1=0

We add all the numbers together, and all the variables

3x^2+18x+1=0

a = 3; b = 18; c = +1;
Δ = b2-4ac
Δ = 182-4·3·1
Δ = 312
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{78}}{2*3}=\frac{-18-2\sqrt{78}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{78}}{2*3}=\frac{-18+2\sqrt{78}}{6}
$