1/2y-4=1/8y

Solution for 1/2y-4=1/8y equation:

1/2y-4=1/8y

We move all terms to the left:

1/2y-4-(1/8y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 8y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

1/2y-(+1/8y)-4=0

We get rid of parentheses

1/2y-1/8y-4=0

We calculate fractions


8y/16y^2+(-2y)/16y^2-4=0

We multiply all the terms by the denominator


8y+(-2y)-4*16y^2=0

Wy multiply elements

-64y^2+8y+(-2y)=0

We get rid of parentheses

-64y^2+8y-2y=0

We add all the numbers together, and all the variables

-64y^2+6y=0

a = -64; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-64)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-64}=\frac{-12}{-128}
=3/32
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-64}=\frac{0}{-128}
=0
$