2y2=2-4y

Solution for 2y2=2-4y equation:

2y^2=2-4y

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

2y^2+4y-2=0

a = 2; b = 4; c = -2;
Δ = b2-4ac
Δ = 42-4·2·(-2)
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2}}{2*2}=\frac{-4-4\sqrt{2}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*2}=\frac{-4+4\sqrt{2}}{4}
$