4y^2=2-y

Solution for 4y^2=2-y equation:

4y^2=2-y

We move all terms to the left:

4y^2-(2-y)=0

We add all the numbers together, and all the variables

4y^2-(-1y+2)=0

We get rid of parentheses

4y^2+1y-2=0

We add all the numbers together, and all the variables

4y^2+y-2=0

a = 4; b = 1; c = -2;
Δ = b2-4ac
Δ = 12-4·4·(-2)
Δ = 33
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{33}}{2*4}=\frac{-1-\sqrt{33}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{33}}{2*4}=\frac{-1+\sqrt{33}}{8}
$