4/x-1+8/3x-1=15/3x+1

Solution for 4/x-1+8/3x-1=15/3x+1 equation:

4/x-1+8/3x-1=15/3x+1

We move all terms to the left:

4/x-1+8/3x-1-(15/3x+1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

4/x+8/3x-(15/3x+1)-2=0

We get rid of parentheses

4/x+8/3x-15/3x-1-2=0

We calculate fractions


12x/3x^2+(-15x+8)/3x^2-1-2=0

We add all the numbers together, and all the variables

12x/3x^2+(-15x+8)/3x^2-3=0

We multiply all the terms by the denominator


12x+(-15x+8)-3*3x^2=0

Wy multiply elements

-9x^2+12x+(-15x+8)=0

We get rid of parentheses

-9x^2+12x-15x+8=0

We add all the numbers together, and all the variables

-9x^2-3x+8=0

a = -9; b = -3; c = +8;
Δ = b2-4ac
Δ = -32-4·(-9)·8
Δ = 297
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{33}}{2*-9}=\frac{3-3\sqrt{33}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{33}}{2*-9}=\frac{3+3\sqrt{33}}{-18}
$