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

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

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

We move all terms to the left:

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


Domain of the equation: 3u!=0

u!=0/3

u!=0

u∈R



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

u∈R


We get rid of parentheses

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

We calculate fractions


(-32u)/24u^2+(-3u)/24u^2+(-9u)/24u^2+3=0

We multiply all the terms by the denominator


(-32u)+(-3u)+(-9u)+3*24u^2=0

Wy multiply elements

72u^2+(-32u)+(-3u)+(-9u)=0

We get rid of parentheses

72u^2-32u-3u-9u=0

We add all the numbers together, and all the variables

72u^2-44u=0

a = 72; b = -44; c = 0;
Δ = b2-4ac
Δ = -442-4·72·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-44}{2*72}=\frac{0}{144}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+44}{2*72}=\frac{88}{144}
=11/18
$