6/x=8/2x+1

Solution for 6/x=8/2x+1 equation:

6/x=8/2x+1

We move all terms to the left:

6/x-(8/2x+1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

6/x-8/2x-1=0

We calculate fractions


12x/2x^2+(-8x)/2x^2-1=0

We multiply all the terms by the denominator


12x+(-8x)-1*2x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+4x=0

a = -2; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-2)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-2}=\frac{-8}{-4}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-2}=\frac{0}{-4}
=0
$