2/3u-3/2=-7/2u-1

Solution for 2/3u-3/2=-7/2u-1 equation:

2/3u-3/2=-7/2u-1

We move all terms to the left:

2/3u-3/2-(-7/2u-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

2/3u+7/2u+1-3/2=0

We calculate fractions


16u/24u^2+21u/24u^2+(-9u)/24u^2+1=0

We multiply all the terms by the denominator


16u+21u+(-9u)+1*24u^2=0

We add all the numbers together, and all the variables

37u+(-9u)+1*24u^2=0

Wy multiply elements

24u^2+37u+(-9u)=0

We get rid of parentheses

24u^2+37u-9u=0

We add all the numbers together, and all the variables

24u^2+28u=0

a = 24; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·24·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*24}=\frac{-56}{48}
=-1+1/6
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*24}=\frac{0}{48}
=0
$