5/x=-2/3x-8

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

5/x=-2/3x-8

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-8)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


15x/3x^2+2x/3x^2+8=0

We multiply all the terms by the denominator


15x+2x+8*3x^2=0

We add all the numbers together, and all the variables

17x+8*3x^2=0

Wy multiply elements

24x^2+17x=0

a = 24; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·24·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*24}=\frac{-34}{48}
=-17/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*24}=\frac{0}{48}
=0
$