Y=-16x^2+48x+6

Solution for Y=-16x^2+48x+6 equation:

=-16Y^2+48Y+6

We move all terms to the left:

-(-16Y^2+48Y+6)=0

We get rid of parentheses

16Y^2-48Y-6=0

a = 16; b = -48; c = -6;
Δ = b2-4ac
Δ = -482-4·16·(-6)
Δ = 2688
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:

$\sqrt{\Delta}=\sqrt{2688}=\sqrt{64*42}=\sqrt{64}*\sqrt{42}=8\sqrt{42}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{42}}{2*16}=\frac{48-8\sqrt{42}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{42}}{2*16}=\frac{48+8\sqrt{42}}{32}
$