6x+13=-6/x

Solution for 6x+13=-6/x equation:

6x+13=-6/x

We move all terms to the left:

6x+13-(-6/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

6x+6/x+13=0

We multiply all the terms by the denominator


6x*x+13*x+6=0

We add all the numbers together, and all the variables

13x+6x*x+6=0

Wy multiply elements

6x^2+13x+6=0

a = 6; b = 13; c = +6;
Δ = b2-4ac
Δ = 132-4·6·6
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{-(13)-5}{2*6}=\frac{-18}{12}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+5}{2*6}=\frac{-8}{12}
=-2/3
$