8/x=3/3x+2

Solution for 8/x=3/3x+2 equation:

8/x=3/3x+2

We move all terms to the left:

8/x-(3/3x+2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

8/x-3/3x-2=0

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-6x^2+24x-3x=0

We add all the numbers together, and all the variables

-6x^2+21x=0

a = -6; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-6)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-6}=\frac{-42}{-12}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-6}=\frac{0}{-12}
=0
$