2/3y+y=31

Solution for 2/3y+y=31 equation:

2/3y+y=31

We move all terms to the left:

2/3y+y-(31)=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+2/3y-31=0

We multiply all the terms by the denominator


y*3y-31*3y+2=0

Wy multiply elements

3y^2-93y+2=0

a = 3; b = -93; c = +2;
Δ = b2-4ac
Δ = -932-4·3·2
Δ = 8625
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:

$\sqrt{\Delta}=\sqrt{8625}=\sqrt{25*345}=\sqrt{25}*\sqrt{345}=5\sqrt{345}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-93)-5\sqrt{345}}{2*3}=\frac{93-5\sqrt{345}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-93)+5\sqrt{345}}{2*3}=\frac{93+5\sqrt{345}}{6}
$