-8/w+4=-1/2w+8+4

Solution for -8/w+4=-1/2w+8+4 equation:

-8/w+4=-1/2w+8+4

We move all terms to the left:

-8/w+4-(-1/2w+8+4)=0


Domain of the equation: w!=0

w∈R



Domain of the equation: 2w+8+4)!=0

We move all terms containing w to the left, all other terms to the right

2w+4)!=-8

w∈R


We add all the numbers together, and all the variables

-8/w-(-1/2w+12)+4=0

We get rid of parentheses

-8/w+1/2w-12+4=0

We calculate fractions


(-16w)/2w^2+w/2w^2-12+4=0

We add all the numbers together, and all the variables

(-16w)/2w^2+w/2w^2-8=0

We multiply all the terms by the denominator


(-16w)+w-8*2w^2=0

We add all the numbers together, and all the variables

w+(-16w)-8*2w^2=0

Wy multiply elements

-16w^2+w+(-16w)=0

We get rid of parentheses

-16w^2+w-16w=0

We add all the numbers together, and all the variables

-16w^2-15w=0

a = -16; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-16)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-16}=\frac{0}{-32}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-16}=\frac{30}{-32}
=-15/16
$