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

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

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

We move all terms to the left:

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


Domain of the equation: 5u!=0

u!=0/5

u!=0

u∈R



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

u∈R


We get rid of parentheses

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

We calculate fractions


24u/40u^2+15u/40u^2+(-15u)/40u^2+1=0

We multiply all the terms by the denominator


24u+15u+(-15u)+1*40u^2=0

We add all the numbers together, and all the variables

39u+(-15u)+1*40u^2=0

Wy multiply elements

40u^2+39u+(-15u)=0

We get rid of parentheses

40u^2+39u-15u=0

We add all the numbers together, and all the variables

40u^2+24u=0

a = 40; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·40·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*40}=\frac{-48}{80}
=-3/5
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*40}=\frac{0}{80}
=0
$