8/x=8/3x+6

Solution for 8/x=8/3x+6 equation:

8/x=8/3x+6

We move all terms to the left:

8/x-(8/3x+6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+6)!=0

x∈R


We get rid of parentheses

8/x-8/3x-6=0

We calculate fractions


24x/3x^2+(-8x)/3x^2-6=0

We multiply all the terms by the denominator


24x+(-8x)-6*3x^2=0

Wy multiply elements

-18x^2+24x+(-8x)=0

We get rid of parentheses

-18x^2+24x-8x=0

We add all the numbers together, and all the variables

-18x^2+16x=0

a = -18; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-18)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-18}=\frac{-32}{-36}
=8/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-18}=\frac{0}{-36}
=0
$