Y=-6x+112-x^2

Solution for Y=-6x+112-x^2 equation:

=-6Y+112-Y^2

We move all terms to the left:

-(-6Y+112-Y^2)=0

We get rid of parentheses

Y^2+6Y-112=0

a = 1; b = 6; c = -112;
Δ = b2-4ac
Δ = 62-4·1·(-112)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-22}{2*1}=\frac{-28}{2}
=-14
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+22}{2*1}=\frac{16}{2}
=8
$