Y=-x^2-6x+45

Solution for Y=-x^2-6x+45 equation:

=-Y^2-6Y+45

We move all terms to the left:

-(-Y^2-6Y+45)=0

We get rid of parentheses

Y^2+6Y-45=0

a = 1; b = 6; c = -45;
Δ = b2-4ac
Δ = 62-4·1·(-45)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{6}}{2*1}=\frac{-6-6\sqrt{6}}{2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{6}}{2*1}=\frac{-6+6\sqrt{6}}{2}
$