2/x-5+5/3x-15=-8

Solution for 2/x-5+5/3x-15=-8 equation:

2/x-5+5/3x-15=-8

We move all terms to the left:

2/x-5+5/3x-15-(-8)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/x+5/3x-12=0

We calculate fractions


6x/3x^2+5x/3x^2-12=0

We multiply all the terms by the denominator


6x+5x-12*3x^2=0

We add all the numbers together, and all the variables

11x-12*3x^2=0

Wy multiply elements

-36x^2+11x=0

a = -36; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-36)·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*-36}=\frac{-22}{-72}
=11/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-36}=\frac{0}{-72}
=0
$