5/x=8/2x-6

Solution for 5/x=8/2x-6 equation:

5/x=8/2x-6

We move all terms to the left:

5/x-(8/2x-6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-6)!=0

x∈R


We get rid of parentheses

5/x-8/2x+6=0

We calculate fractions


10x/2x^2+(-8x)/2x^2+6=0

We multiply all the terms by the denominator


10x+(-8x)+6*2x^2=0

Wy multiply elements

12x^2+10x+(-8x)=0

We get rid of parentheses

12x^2+10x-8x=0

We add all the numbers together, and all the variables

12x^2+2x=0

a = 12; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·12·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*12}=\frac{-4}{24}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*12}=\frac{0}{24}
=0
$