3/x=3/5x+4

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

3/x=3/5x+4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


15x/5x^2+(-3x)/5x^2-4=0

We multiply all the terms by the denominator


15x+(-3x)-4*5x^2=0

Wy multiply elements

-20x^2+15x+(-3x)=0

We get rid of parentheses

-20x^2+15x-3x=0

We add all the numbers together, and all the variables

-20x^2+12x=0

a = -20; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-20)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-20}=\frac{-24}{-40}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-20}=\frac{0}{-40}
=0
$