3/2w-3=2/w+4

Solution for 3/2w-3=2/w+4 equation:

3/2w-3=2/w+4

We move all terms to the left:

3/2w-3-(2/w+4)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: w+4)!=0

w∈R


We get rid of parentheses

3/2w-2/w-4-3=0

We calculate fractions


3w/2w^2+(-4w)/2w^2-4-3=0

We add all the numbers together, and all the variables

3w/2w^2+(-4w)/2w^2-7=0

We multiply all the terms by the denominator


3w+(-4w)-7*2w^2=0

Wy multiply elements

-14w^2+3w+(-4w)=0

We get rid of parentheses

-14w^2+3w-4w=0

We add all the numbers together, and all the variables

-14w^2-1w=0

a = -14; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-14)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-14}=\frac{0}{-28}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-14}=\frac{2}{-28}
=-1/14
$