1/2w-5=1/4w-1

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

1/2w-5=1/4w-1

We move all terms to the left:

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


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 4w-1)!=0

w∈R


We get rid of parentheses

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

We calculate fractions


4w/8w^2+(-2w)/8w^2+1-5=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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