8/x+22=2/3x

Solution for 8/x+22=2/3x equation:

8/x+22=2/3x

We move all terms to the left:

8/x+22-(2/3x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8/x-(+2/3x)+22=0

We get rid of parentheses

8/x-2/3x+22=0

We calculate fractions


24x/3x^2+(-2x)/3x^2+22=0

We multiply all the terms by the denominator


24x+(-2x)+22*3x^2=0

Wy multiply elements

66x^2+24x+(-2x)=0

We get rid of parentheses

66x^2+24x-2x=0

We add all the numbers together, and all the variables

66x^2+22x=0

a = 66; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·66·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*66}=\frac{-44}{132}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*66}=\frac{0}{132}
=0
$