4/3x+5=-2/x

Solution for 4/3x+5=-2/x equation:

4/3x+5=-2/x

We move all terms to the left:

4/3x+5-(-2/x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

4/3x+2/x+5=0

We calculate fractions


4x/3x^2+6x/3x^2+5=0

We multiply all the terms by the denominator


4x+6x+5*3x^2=0

We add all the numbers together, and all the variables

10x+5*3x^2=0

Wy multiply elements

15x^2+10x=0

a = 15; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·15·0
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*15}=\frac{-20}{30}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*15}=\frac{0}{30}
=0
$