3/2u-4/3=-4/3u-1

Solution for 3/2u-4/3=-4/3u-1 equation:

3/2u-4/3=-4/3u-1

We move all terms to the left:

3/2u-4/3-(-4/3u-1)=0


Domain of the equation: 2u!=0

u!=0/2

u!=0

u∈R



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

u∈R


We get rid of parentheses

3/2u+4/3u+1-4/3=0

We calculate fractions


81u/54u^2+8u/54u^2+(-8u)/54u^2+1=0

We multiply all the terms by the denominator


81u+8u+(-8u)+1*54u^2=0

We add all the numbers together, and all the variables

89u+(-8u)+1*54u^2=0

Wy multiply elements

54u^2+89u+(-8u)=0

We get rid of parentheses

54u^2+89u-8u=0

We add all the numbers together, and all the variables

54u^2+81u=0

a = 54; b = 81; c = 0;
Δ = b2-4ac
Δ = 812-4·54·0
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-81}{2*54}=\frac{-162}{108}
=-1+1/2
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+81}{2*54}=\frac{0}{108}
=0
$