Y=-4x^2+2x+2

Solution for Y=-4x^2+2x+2 equation:

=-4Y^2+2Y+2

We move all terms to the left:

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

We get rid of parentheses

4Y^2-2Y-2=0

a = 4; b = -2; c = -2;
Δ = b2-4ac
Δ = -22-4·4·(-2)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*4}=\frac{-4}{8}
=-1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*4}=\frac{8}{8}
=1
$