y+1/3y+1=9

Solution for y+1/3y+1=9 equation:

y+1/3y+1=9

We move all terms to the left:

y+1/3y+1-(9)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

y+1/3y-8=0

We multiply all the terms by the denominator


y*3y-8*3y+1=0

Wy multiply elements

3y^2-24y+1=0

a = 3; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·3·1
Δ = 564
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:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{141}}{2*3}=\frac{24-2\sqrt{141}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{141}}{2*3}=\frac{24+2\sqrt{141}}{6}
$