2x+13=(1/3x)-7

Solution for 2x+13=(1/3x)-7 equation:

2x+13=(1/3x)-7

We move all terms to the left:

2x+13-((1/3x)-7)=0


Domain of the equation: 3x)-7)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-((+1/3x)-7)+13=0

We multiply all the terms by the denominator


2x*3x)-7)-((+13*3x)-7)+1=0

Wy multiply elements

6x^2+39x=0

a = 6; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·6·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-39}{2*6}=\frac{-78}{12}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*6}=\frac{0}{12}
=0
$