5x-39=8/x

Solution for 5x-39=8/x equation:

5x-39=8/x

We move all terms to the left:

5x-39-(8/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

5x-(+8/x)-39=0

We get rid of parentheses

5x-8/x-39=0

We multiply all the terms by the denominator


5x*x-39*x-8=0

We add all the numbers together, and all the variables

-39x+5x*x-8=0

Wy multiply elements

5x^2-39x-8=0

a = 5; b = -39; c = -8;
Δ = b2-4ac
Δ = -392-4·5·(-8)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-41}{2*5}=\frac{-2}{10}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+41}{2*5}=\frac{80}{10}
=8
$