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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


24x/12x^2+(-16x)/12x^2+1+1=0

We add all the numbers together, and all the variables

24x/12x^2+(-16x)/12x^2+2=0

We multiply all the terms by the denominator


24x+(-16x)+2*12x^2=0

Wy multiply elements

24x^2+24x+(-16x)=0

We get rid of parentheses

24x^2+24x-16x=0

We add all the numbers together, and all the variables

24x^2+8x=0

a = 24; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·24·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*24}=\frac{-16}{48}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*24}=\frac{0}{48}
=0
$