0.2y=0.4y^2-1

Solution for 0.2y=0.4y^2-1 equation:

0.2y=0.4y^2-1

We move all terms to the left:

0.2y-(0.4y^2-1)=0

We get rid of parentheses

-0.4y^2+0.2y+1=0

a = -0.4; b = 0.2; c = +1;
Δ = b2-4ac
Δ = 0.22-4·(-0.4)·1
Δ = 1.64
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{-(0.2)-\sqrt{1.64}}{2*-0.4}=\frac{-0.2-\sqrt{1.64}}{-0.8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.2)+\sqrt{1.64}}{2*-0.4}=\frac{-0.2+\sqrt{1.64}}{-0.8}
$