3/2w-1/2=-2/3w-5

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

3/2w-1/2=-2/3w-5

We move all terms to the left:

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


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 3w-5)!=0

w∈R


We get rid of parentheses

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

We calculate fractions


9w/24w^2+16w/24w^2+(-3w)/24w^2+5=0

We multiply all the terms by the denominator


9w+16w+(-3w)+5*24w^2=0

We add all the numbers together, and all the variables

25w+(-3w)+5*24w^2=0

Wy multiply elements

120w^2+25w+(-3w)=0

We get rid of parentheses

120w^2+25w-3w=0

We add all the numbers together, and all the variables

120w^2+22w=0

a = 120; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·120·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*120}=\frac{-44}{240}
=-11/60
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*120}=\frac{0}{240}
=0
$