3y2=1-y

Solution for 3y2=1-y equation:

3y^2=1-y

We move all terms to the left:

3y^2-(1-y)=0

We add all the numbers together, and all the variables

3y^2-(-1y+1)=0

We get rid of parentheses

3y^2+1y-1=0

We add all the numbers together, and all the variables

3y^2+y-1=0

a = 3; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·3·(-1)
Δ = 13
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{-(1)-\sqrt{13}}{2*3}=\frac{-1-\sqrt{13}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{13}}{2*3}=\frac{-1+\sqrt{13}}{6}
$