5/3u-3/2=-3/2u-1

Solution for 5/3u-3/2=-3/2u-1 equation:

5/3u-3/2=-3/2u-1

We move all terms to the left:

5/3u-3/2-(-3/2u-1)=0


Domain of the equation: 3u!=0

u!=0/3

u!=0

u∈R



Domain of the equation: 2u-1)!=0

u∈R


We get rid of parentheses

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

We calculate fractions


40u/24u^2+9u/24u^2+(-9u)/24u^2+1=0

We multiply all the terms by the denominator


40u+9u+(-9u)+1*24u^2=0

We add all the numbers together, and all the variables

49u+(-9u)+1*24u^2=0

Wy multiply elements

24u^2+49u+(-9u)=0

We get rid of parentheses

24u^2+49u-9u=0

We add all the numbers together, and all the variables

24u^2+40u=0

a = 24; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·24·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*24}=\frac{-80}{48}
=-1+2/3
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*24}=\frac{0}{48}
=0
$