6x-13=5/x

Solution for 6x-13=5/x equation:

6x-13=5/x

We move all terms to the left:

6x-13-(5/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(+5/x)-13=0

We get rid of parentheses

6x-5/x-13=0

We multiply all the terms by the denominator


6x*x-13*x-5=0

We add all the numbers together, and all the variables

-13x+6x*x-5=0

Wy multiply elements

6x^2-13x-5=0

a = 6; b = -13; c = -5;
Δ = b2-4ac
Δ = -132-4·6·(-5)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-17}{2*6}=\frac{-4}{12}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+17}{2*6}=\frac{30}{12}
=2+1/2
$