x+8/3x+4=x+8/2x-1

Solution for x+8/3x+4=x+8/2x-1 equation:

x+8/3x+4=x+8/2x-1

We move all terms to the left:

x+8/3x+4-(x+8/2x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

x+8/3x-x-8/2x+1+4=0

We calculate fractions


x-x+16x/6x^2+(-24x)/6x^2+1+4=0

We add all the numbers together, and all the variables

16x/6x^2+(-24x)/6x^2+5=0

We multiply all the terms by the denominator


16x+(-24x)+5*6x^2=0

Wy multiply elements

30x^2+16x+(-24x)=0

We get rid of parentheses

30x^2+16x-24x=0

We add all the numbers together, and all the variables

30x^2-8x=0

a = 30; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·30·0
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*30}=\frac{0}{60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*30}=\frac{16}{60}
=4/15
$