32/2x+3=40/3x-1

Solution for 32/2x+3=40/3x-1 equation:

32/2x+3=40/3x-1

We move all terms to the left:

32/2x+3-(40/3x-1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x-1)!=0

x∈R


We get rid of parentheses

32/2x-40/3x+1+3=0

We calculate fractions


96x/6x^2+(-80x)/6x^2+1+3=0

We add all the numbers together, and all the variables

96x/6x^2+(-80x)/6x^2+4=0

We multiply all the terms by the denominator


96x+(-80x)+4*6x^2=0

Wy multiply elements

24x^2+96x+(-80x)=0

We get rid of parentheses

24x^2+96x-80x=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{-32}{48}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*24}=\frac{0}{48}
=0
$