8/2w+1=3/w

Solution for 8/2w+1=3/w equation:

8/2w+1=3/w

We move all terms to the left:

8/2w+1-(3/w)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

8/2w-(+3/w)+1=0

We get rid of parentheses

8/2w-3/w+1=0

We calculate fractions


8w/2w^2+(-6w)/2w^2+1=0

We multiply all the terms by the denominator


8w+(-6w)+1*2w^2=0

Wy multiply elements

2w^2+8w+(-6w)=0

We get rid of parentheses

2w^2+8w-6w=0

We add all the numbers together, and all the variables

2w^2+2w=0

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

$\sqrt{\Delta}=\sqrt{4}=2$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*2}=\frac{-4}{4}
=-1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*2}=\frac{0}{4}
=0
$