4/8w+4=8w

Solution for 4/8w+4=8w equation:

4/8w+4=8w

We move all terms to the left:

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


Domain of the equation: 8w!=0

w!=0/8

w!=0

w∈R


We add all the numbers together, and all the variables

-8w+4/8w+4=0

We multiply all the terms by the denominator


-8w*8w+4*8w+4=0

Wy multiply elements

-64w^2+32w+4=0

a = -64; b = 32; c = +4;
Δ = b2-4ac
Δ = 322-4·(-64)·4
Δ = 2048
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:

$\sqrt{\Delta}=\sqrt{2048}=\sqrt{1024*2}=\sqrt{1024}*\sqrt{2}=32\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32\sqrt{2}}{2*-64}=\frac{-32-32\sqrt{2}}{-128}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32\sqrt{2}}{2*-64}=\frac{-32+32\sqrt{2}}{-128}
$