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

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

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

We move all terms to the left:

3/x+2-(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

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

We get rid of parentheses

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

We calculate fractions


15x/5x^2+(-4x)/5x^2+2=0

We multiply all the terms by the denominator


15x+(-4x)+2*5x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

10x^2+11x=0

a = 10; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·10·0
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*10}=\frac{-22}{20}
=-1+1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*10}=\frac{0}{20}
=0
$