2/3x-3=5-3/5x

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

2/3x-3=5-3/5x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

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

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

We get rid of parentheses

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

We calculate fractions


10x/15x^2+9x/15x^2-5-3=0

We add all the numbers together, and all the variables

10x/15x^2+9x/15x^2-8=0

We multiply all the terms by the denominator


10x+9x-8*15x^2=0

We add all the numbers together, and all the variables

19x-8*15x^2=0

Wy multiply elements

-120x^2+19x=0

a = -120; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-120)·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*-120}=\frac{-38}{-240}
=19/120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-120}=\frac{0}{-240}
=0
$