1/4w+4=3/2w

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

1/4w+4=3/2w

We move all terms to the left:

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


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 2w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


2w+(-12w)+4*8w^2=0

Wy multiply elements

32w^2+2w+(-12w)=0

We get rid of parentheses

32w^2+2w-12w=0

We add all the numbers together, and all the variables

32w^2-10w=0

a = 32; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·32·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*32}=\frac{0}{64}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*32}=\frac{20}{64}
=5/16
$