2y+y+1/3y=150

Solution for 2y+y+1/3y=150 equation:

2y+y+1/3y=150

We move all terms to the left:

2y+y+1/3y-(150)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

3y+1/3y-150=0

We multiply all the terms by the denominator


3y*3y-150*3y+1=0

Wy multiply elements

9y^2-450y+1=0

a = 9; b = -450; c = +1;
Δ = b2-4ac
Δ = -4502-4·9·1
Δ = 202464
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:

$\sqrt{\Delta}=\sqrt{202464}=\sqrt{144*1406}=\sqrt{144}*\sqrt{1406}=12\sqrt{1406}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-450)-12\sqrt{1406}}{2*9}=\frac{450-12\sqrt{1406}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-450)+12\sqrt{1406}}{2*9}=\frac{450+12\sqrt{1406}}{18}
$