y+2/3y=16

Solution for y+2/3y=16 equation:

y+2/3y=16

We move all terms to the left:

y+2/3y-(16)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We multiply all the terms by the denominator


y*3y-16*3y+2=0

Wy multiply elements

3y^2-48y+2=0

a = 3; b = -48; c = +2;
Δ = b2-4ac
Δ = -482-4·3·2
Δ = 2280
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:

$\sqrt{\Delta}=\sqrt{2280}=\sqrt{4*570}=\sqrt{4}*\sqrt{570}=2\sqrt{570}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{570}}{2*3}=\frac{48-2\sqrt{570}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{570}}{2*3}=\frac{48+2\sqrt{570}}{6}
$