1/3x+5=-2x-2

Solution for 1/3x+5=-2x-2 equation:

1/3x+5=-2x-2

We move all terms to the left:

1/3x+5-(-2x-2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x+2x+2+5=0

We multiply all the terms by the denominator


2x*3x+2*3x+5*3x+1=0

Wy multiply elements

6x^2+6x+15x+1=0

We add all the numbers together, and all the variables

6x^2+21x+1=0

a = 6; b = 21; c = +1;
Δ = b2-4ac
Δ = 212-4·6·1
Δ = 417
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{417}}{2*6}=\frac{-21-\sqrt{417}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{417}}{2*6}=\frac{-21+\sqrt{417}}{12}
$