1/2w+4=5/w-2

Solution for 1/2w+4=5/w-2 equation:

1/2w+4=5/w-2

We move all terms to the left:

1/2w+4-(5/w-2)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: w-2)!=0

w∈R


We get rid of parentheses

1/2w-5/w+2+4=0

We calculate fractions


w/2w^2+(-10w)/2w^2+2+4=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

12w^2+w+(-10w)=0

We get rid of parentheses

12w^2+w-10w=0

We add all the numbers together, and all the variables

12w^2-9w=0

a = 12; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·12·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*12}=\frac{0}{24}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*12}=\frac{18}{24}
=3/4
$