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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


25x/15x^2+(-6x)/15x^2-3-4=0

We add all the numbers together, and all the variables

25x/15x^2+(-6x)/15x^2-7=0

We multiply all the terms by the denominator


25x+(-6x)-7*15x^2=0

Wy multiply elements

-105x^2+25x+(-6x)=0

We get rid of parentheses

-105x^2+25x-6x=0

We add all the numbers together, and all the variables

-105x^2+19x=0

a = -105; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-105)·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*-105}=\frac{-38}{-210}
=19/105
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-105}=\frac{0}{-210}
=0
$