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

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

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

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

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

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

We get rid of parentheses

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

We calculate fractions


20x/5x^2+(-2x)/5x^2-3=0

We multiply all the terms by the denominator


20x+(-2x)-3*5x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-15x^2+18x=0

a = -15; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-15)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-15}=\frac{-36}{-30}
=1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-15}=\frac{0}{-30}
=0
$