-5/3x+1=2/2x-3

Solution for -5/3x+1=2/2x-3 equation:

-5/3x+1=2/2x-3

We move all terms to the left:

-5/3x+1-(2/2x-3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

-5/3x-2/2x+3+1=0

We calculate fractions


(-10x)/6x^2+(-6x)/6x^2+3+1=0

We add all the numbers together, and all the variables

(-10x)/6x^2+(-6x)/6x^2+4=0

We multiply all the terms by the denominator


(-10x)+(-6x)+4*6x^2=0

Wy multiply elements

24x^2+(-10x)+(-6x)=0

We get rid of parentheses

24x^2-10x-6x=0

We add all the numbers together, and all the variables

24x^2-16x=0

a = 24; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·24·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*24}=\frac{32}{48}
=2/3
$