2/3y+y-4=31=

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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-35=0

We multiply all the terms by the denominator


y*3y-35*3y+2=0

Wy multiply elements

3y^2-105y+2=0

a = 3; b = -105; c = +2;
Δ = b2-4ac
Δ = -1052-4·3·2
Δ = 11001
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{-(-105)-\sqrt{11001}}{2*3}=\frac{105-\sqrt{11001}}{6}
$


$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{11001}}{2*3}=\frac{105+\sqrt{11001}}{6}
$

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