20/2x-6=39/x+8

Solution for 20/2x-6=39/x+8 equation:

20/2x-6=39/x+8

We move all terms to the left:

20/2x-6-(39/x+8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x+8)!=0

x∈R


We get rid of parentheses

20/2x-39/x-8-6=0

We calculate fractions


20x/2x^2+(-78x)/2x^2-8-6=0

We add all the numbers together, and all the variables

20x/2x^2+(-78x)/2x^2-14=0

We multiply all the terms by the denominator


20x+(-78x)-14*2x^2=0

Wy multiply elements

-28x^2+20x+(-78x)=0

We get rid of parentheses

-28x^2+20x-78x=0

We add all the numbers together, and all the variables

-28x^2-58x=0

a = -28; b = -58; c = 0;
Δ = b2-4ac
Δ = -582-4·(-28)·0
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-58}{2*-28}=\frac{0}{-56}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+58}{2*-28}=\frac{116}{-56}
=-2+1/14
$