8/3x-5=6/x+5

Solution for 8/3x-5=6/x+5 equation:

8/3x-5=6/x+5

We move all terms to the left:

8/3x-5-(6/x+5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x+5)!=0

x∈R


We get rid of parentheses

8/3x-6/x-5-5=0

We calculate fractions


8x/3x^2+(-18x)/3x^2-5-5=0

We add all the numbers together, and all the variables

8x/3x^2+(-18x)/3x^2-10=0

We multiply all the terms by the denominator


8x+(-18x)-10*3x^2=0

Wy multiply elements

-30x^2+8x+(-18x)=0

We get rid of parentheses

-30x^2+8x-18x=0

We add all the numbers together, and all the variables

-30x^2-10x=0

a = -30; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-30)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-30}=\frac{0}{-60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-30}=\frac{20}{-60}
=-1/3
$