4(w-2)=1/2w

Solution for 4(w-2)=1/2w equation:

4(w-2)=1/2w

We move all terms to the left:

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


Domain of the equation: 2w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

4w-1/2w-8=0

We multiply all the terms by the denominator


4w*2w-8*2w-1=0

Wy multiply elements

8w^2-16w-1=0

a = 8; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·8·(-1)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-12\sqrt{2}}{2*8}=\frac{16-12\sqrt{2}}{16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+12\sqrt{2}}{2*8}=\frac{16+12\sqrt{2}}{16}
$