3/w+5=1/2w

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

3/w+5=1/2w

We move all terms to the left:

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


Domain of the equation: w!=0

w∈R



Domain of the equation: 2w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


6w/2w^2+(-w)/2w^2+5=0

We add all the numbers together, and all the variables

6w/2w^2+(-1w)/2w^2+5=0

We multiply all the terms by the denominator


6w+(-1w)+5*2w^2=0

Wy multiply elements

10w^2+6w+(-1w)=0

We get rid of parentheses

10w^2+6w-1w=0

We add all the numbers together, and all the variables

10w^2+5w=0

a = 10; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·10·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*10}=\frac{-10}{20}
=-1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*10}=\frac{0}{20}
=0
$