1/3y=48+y

Solution for 1/3y=48+y equation:

1/3y=48+y

We move all terms to the left:

1/3y-(48+y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

1/3y-(y+48)=0

We get rid of parentheses

1/3y-y-48=0

We multiply all the terms by the denominator


-y*3y-48*3y+1=0

Wy multiply elements

-3y^2-144y+1=0

a = -3; b = -144; c = +1;
Δ = b2-4ac
Δ = -1442-4·(-3)·1
Δ = 20748
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20748}=\sqrt{4*5187}=\sqrt{4}*\sqrt{5187}=2\sqrt{5187}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-2\sqrt{5187}}{2*-3}=\frac{144-2\sqrt{5187}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+2\sqrt{5187}}{2*-3}=\frac{144+2\sqrt{5187}}{-6}
$