1/4w-9=1/8w-1

Solution for 1/4w-9=1/8w-1 equation:

1/4w-9=1/8w-1

We move all terms to the left:

1/4w-9-(1/8w-1)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 8w-1)!=0

w∈R


We get rid of parentheses

1/4w-1/8w+1-9=0

We calculate fractions


8w/32w^2+(-4w)/32w^2+1-9=0

We add all the numbers together, and all the variables

8w/32w^2+(-4w)/32w^2-8=0

We multiply all the terms by the denominator


8w+(-4w)-8*32w^2=0

Wy multiply elements

-256w^2+8w+(-4w)=0

We get rid of parentheses

-256w^2+8w-4w=0

We add all the numbers together, and all the variables

-256w^2+4w=0

a = -256; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-256)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-256}=\frac{-8}{-512}
=1/64
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-256}=\frac{0}{-512}
=0
$