1/2w+4=3/4w

Solution for 1/2w+4=3/4w equation:

1/2w+4=3/4w

We move all terms to the left:

1/2w+4-(3/4w)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 4w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

1/2w-(+3/4w)+4=0

We get rid of parentheses

1/2w-3/4w+4=0

We calculate fractions


4w/8w^2+(-6w)/8w^2+4=0

We multiply all the terms by the denominator


4w+(-6w)+4*8w^2=0

Wy multiply elements

32w^2+4w+(-6w)=0

We get rid of parentheses

32w^2+4w-6w=0

We add all the numbers together, and all the variables

32w^2-2w=0

a = 32; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·32·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*32}=\frac{0}{64}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*32}=\frac{4}{64}
=1/16
$