2/x+3=4/5x

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

2/x+3=4/5x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


10x/5x^2+(-4x)/5x^2+3=0

We multiply all the terms by the denominator


10x+(-4x)+3*5x^2=0

Wy multiply elements

15x^2+10x+(-4x)=0

We get rid of parentheses

15x^2+10x-4x=0

We add all the numbers together, and all the variables

15x^2+6x=0

a = 15; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·15·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*15}=\frac{-12}{30}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*15}=\frac{0}{30}
=0
$