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

Solution for x+(x+5)+1/3x=0 equation:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2+3x^2+15x+1=0

We add all the numbers together, and all the variables

6x^2+15x+1=0

a = 6; b = 15; c = +1;
Δ = b2-4ac
Δ = 152-4·6·1
Δ = 201
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{-(15)-\sqrt{201}}{2*6}=\frac{-15-\sqrt{201}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{201}}{2*6}=\frac{-15+\sqrt{201}}{12}
$