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

Solution for 6/x-1+8/3x+1=15/3x+1 equation:

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

We move all terms to the left:

6/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

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

We get rid of parentheses

6/x+8/3x-15/3x-1=0

We calculate fractions


18x/3x^2+(-15x+8)/3x^2-1=0

We multiply all the terms by the denominator


18x+(-15x+8)-1*3x^2=0

Wy multiply elements

-3x^2+18x+(-15x+8)=0

We get rid of parentheses

-3x^2+18x-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}
$