5/3x+8=-2/x-1

Solution for 5/3x+8=-2/x-1 equation:

5/3x+8=-2/x-1

We move all terms to the left:

5/3x+8-(-2/x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

5/3x+2/x+1+8=0

We calculate fractions


5x/3x^2+6x/3x^2+1+8=0

We add all the numbers together, and all the variables

5x/3x^2+6x/3x^2+9=0

We multiply all the terms by the denominator


5x+6x+9*3x^2=0

We add all the numbers together, and all the variables

11x+9*3x^2=0

Wy multiply elements

27x^2+11x=0

a = 27; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·27·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*27}=\frac{-22}{54}
=-11/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*27}=\frac{0}{54}
=0
$