3/x+4=5/3x

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

3/x+4=5/3x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


9x/3x^2+(-5x)/3x^2+4=0

We multiply all the terms by the denominator


9x+(-5x)+4*3x^2=0

Wy multiply elements

12x^2+9x+(-5x)=0

We get rid of parentheses

12x^2+9x-5x=0

We add all the numbers together, and all the variables

12x^2+4x=0

a = 12; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·12·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*12}=\frac{-8}{24}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*12}=\frac{0}{24}
=0
$