38+1/3y=2-y

Solution for 38+1/3y=2-y equation:

38+1/3y=2-y

We move all terms to the left:

38+1/3y-(2-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-(-1y+2)+38=0

We get rid of parentheses

1/3y+1y-2+38=0

We multiply all the terms by the denominator


1y*3y-2*3y+38*3y+1=0

Wy multiply elements

3y^2-6y+114y+1=0

We add all the numbers together, and all the variables

3y^2+108y+1=0

a = 3; b = 108; c = +1;
Δ = b2-4ac
Δ = 1082-4·3·1
Δ = 11652
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:

$\sqrt{\Delta}=\sqrt{11652}=\sqrt{4*2913}=\sqrt{4}*\sqrt{2913}=2\sqrt{2913}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-2\sqrt{2913}}{2*3}=\frac{-108-2\sqrt{2913}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+2\sqrt{2913}}{2*3}=\frac{-108+2\sqrt{2913}}{6}
$