Y=-16x^2+63x+4

Solution for Y=-16x^2+63x+4 equation:

=-16Y^2+63Y+4

We move all terms to the left:

-(-16Y^2+63Y+4)=0

We get rid of parentheses

16Y^2-63Y-4=0

a = 16; b = -63; c = -4;
Δ = b2-4ac
Δ = -632-4·16·(-4)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-65}{2*16}=\frac{-2}{32}
=-1/16
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+65}{2*16}=\frac{128}{32}
=4
$