-1/3y+y=1

Solution for -1/3y+y=1 equation:

-1/3y+y=1

We move all terms to the left:

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

We multiply all the terms by the denominator


y*3y-1*3y-1=0

Wy multiply elements

3y^2-3y-1=0

a = 3; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·3·(-1)
Δ = 21
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{-(-3)-\sqrt{21}}{2*3}=\frac{3-\sqrt{21}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{21}}{2*3}=\frac{3+\sqrt{21}}{6}
$