Y=x^2+44x-384

Solution for Y=x^2+44x-384 equation:

=Y^2+44Y-384

We move all terms to the left:

-(Y^2+44Y-384)=0

We get rid of parentheses

-Y^2-44Y+384=0

We add all the numbers together, and all the variables

-1Y^2-44Y+384=0

a = -1; b = -44; c = +384;
Δ = b2-4ac
Δ = -442-4·(-1)·384
Δ = 3472
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:

$\sqrt{\Delta}=\sqrt{3472}=\sqrt{16*217}=\sqrt{16}*\sqrt{217}=4\sqrt{217}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{217}}{2*-1}=\frac{44-4\sqrt{217}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{217}}{2*-1}=\frac{44+4\sqrt{217}}{-2}
$