Y=-16x^2+252x+127

Solution for Y=-16x^2+252x+127 equation:

=-16Y^2+252Y+127

We move all terms to the left:

-(-16Y^2+252Y+127)=0

We get rid of parentheses

16Y^2-252Y-127=0

a = 16; b = -252; c = -127;
Δ = b2-4ac
Δ = -2522-4·16·(-127)
Δ = 71632
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:

$\sqrt{\Delta}=\sqrt{71632}=\sqrt{1936*37}=\sqrt{1936}*\sqrt{37}=44\sqrt{37}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-44\sqrt{37}}{2*16}=\frac{252-44\sqrt{37}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+44\sqrt{37}}{2*16}=\frac{252+44\sqrt{37}}{32}
$