1/w+2=w-3/w

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

1/w+2=w-3/w

We move all terms to the left:

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


Domain of the equation: 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

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-w*w+2*w+1+3=0

We add all the numbers together, and all the variables

2w-w*w+4=0

Wy multiply elements

-1w^2+2w+4=0

a = -1; b = 2; c = +4;
Δ = b2-4ac
Δ = 22-4·(-1)·4
Δ = 20
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{5}}{2*-1}=\frac{-2-2\sqrt{5}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{5}}{2*-1}=\frac{-2+2\sqrt{5}}{-2}
$