1/3y=8+1/8y

Solution for 1/3y=8+1/8y equation:

1/3y=8+1/8y

We move all terms to the left:

1/3y-(8+1/8y)=0


Domain of the equation: 3y!=0

y!=0/3

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

1/3y-(1/8y+8)=0

We get rid of parentheses

1/3y-1/8y-8=0

We calculate fractions


8y/24y^2+(-3y)/24y^2-8=0

We multiply all the terms by the denominator


8y+(-3y)-8*24y^2=0

Wy multiply elements

-192y^2+8y+(-3y)=0

We get rid of parentheses

-192y^2+8y-3y=0

We add all the numbers together, and all the variables

-192y^2+5y=0

a = -192; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-192)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-192}=\frac{-10}{-384}
=5/192
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-192}=\frac{0}{-384}
=0
$