1/4w+1/2w+5=1

Solution for 1/4w+1/2w+5=1 equation:

1/4w+1/2w+5=1

We move all terms to the left:

1/4w+1/2w+5-(1)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We add all the numbers together, and all the variables

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

We calculate fractions


2w/8w^2+4w/8w^2+4=0

We multiply all the terms by the denominator


2w+4w+4*8w^2=0

We add all the numbers together, and all the variables

6w+4*8w^2=0

Wy multiply elements

32w^2+6w=0

a = 32; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·32·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*32}=\frac{-12}{64}
=-3/16
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*32}=\frac{0}{64}
=0
$