Y=-16x^2+12x-2

Solution for Y=-16x^2+12x-2 equation:

=-16Y^2+12Y-2

We move all terms to the left:

-(-16Y^2+12Y-2)=0

We get rid of parentheses

16Y^2-12Y+2=0

a = 16; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·16·2
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4}{2*16}=\frac{8}{32}
=1/4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4}{2*16}=\frac{16}{32}
=1/2
$