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^2-1=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-3x^2+12x-15x+8=0

We add all the numbers together, and all the variables

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

a = -3; b = -3; c = +8;
Δ = b2-4ac
Δ = -32-4·(-3)·8
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{105}}{2*-3}=\frac{3-\sqrt{105}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{105}}{2*-3}=\frac{3+\sqrt{105}}{-6}
$