Y=-16x^2+6

Solution for Y=-16x^2+6 equation:

=-16Y^2+6

We move all terms to the left:

-(-16Y^2+6)=0

We get rid of parentheses

16Y^2-6=0

a = 16; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·16·(-6)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*16}=\frac{0-8\sqrt{6}}{32}
=-\frac{8\sqrt{6}}{32}
=-\frac{\sqrt{6}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*16}=\frac{0+8\sqrt{6}}{32}
=\frac{8\sqrt{6}}{32}
=\frac{\sqrt{6}}{4}
$