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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

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

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

We get rid of parentheses

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

We calculate fractions


6x/15x^2+(-25x)/15x^2-4=0

We multiply all the terms by the denominator


6x+(-25x)-4*15x^2=0

Wy multiply elements

-60x^2+6x+(-25x)=0

We get rid of parentheses

-60x^2+6x-25x=0

We add all the numbers together, and all the variables

-60x^2-19x=0

a = -60; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·(-60)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*-60}=\frac{38}{-120}
=-19/60
$