8/x=4/3x+1

Solution for 8/x=4/3x+1 equation:

8/x=4/3x+1

We move all terms to the left:

8/x-(4/3x+1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

8/x-4/3x-1=0

We calculate fractions


24x/3x^2+(-4x)/3x^2-1=0

We multiply all the terms by the denominator


24x+(-4x)-1*3x^2=0

Wy multiply elements

-3x^2+24x+(-4x)=0

We get rid of parentheses

-3x^2+24x-4x=0

We add all the numbers together, and all the variables

-3x^2+20x=0

a = -3; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-3)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-3}=\frac{-40}{-6}
=6+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-3}=\frac{0}{-6}
=0
$