4/x-5-1/3=-8/3x-15

Solution for 4/x-5-1/3=-8/3x-15 equation:

4/x-5-1/3=-8/3x-15

We move all terms to the left:

4/x-5-1/3-(-8/3x-15)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-15)!=0

x∈R


We get rid of parentheses

4/x+8/3x+15-5-1/3=0

We calculate fractions


108x/27x^2+8x/27x^2+(-x)/27x^2+15-5=0

We add all the numbers together, and all the variables

108x/27x^2+8x/27x^2+(-1x)/27x^2+15-5=0

We add all the numbers together, and all the variables

108x/27x^2+8x/27x^2+(-1x)/27x^2+10=0

We multiply all the terms by the denominator


108x+8x+(-1x)+10*27x^2=0

We add all the numbers together, and all the variables

116x+(-1x)+10*27x^2=0

Wy multiply elements

270x^2+116x+(-1x)=0

We get rid of parentheses

270x^2+116x-1x=0

We add all the numbers together, and all the variables

270x^2+115x=0

a = 270; b = 115; c = 0;
Δ = b2-4ac
Δ = 1152-4·270·0
Δ = 13225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13225}=115$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(115)-115}{2*270}=\frac{-230}{540}
=-23/54
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(115)+115}{2*270}=\frac{0}{540}
=0
$