2/3y+y-4=-31

Solution for 2/3y+y-4=-31 equation:

2/3y+y-4=-31

We move all terms to the left:

2/3y+y-4-(-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+27=0

We multiply all the terms by the denominator


y*3y+27*3y+2=0

Wy multiply elements

3y^2+81y+2=0

a = 3; b = 81; c = +2;
Δ = b2-4ac
Δ = 812-4·3·2
Δ = 6537
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-\sqrt{6537}}{2*3}=\frac{-81-\sqrt{6537}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+\sqrt{6537}}{2*3}=\frac{-81+\sqrt{6537}}{6}
$