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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


5x/3x^2+(-6x)/3x^2-2-5=0

We add all the numbers together, and all the variables

5x/3x^2+(-6x)/3x^2-7=0

We multiply all the terms by the denominator


5x+(-6x)-7*3x^2=0

Wy multiply elements

-21x^2+5x+(-6x)=0

We get rid of parentheses

-21x^2+5x-6x=0

We add all the numbers together, and all the variables

-21x^2-1x=0

a = -21; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-21)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-21}=\frac{0}{-42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-21}=\frac{2}{-42}
=-1/21
$