Y=-x^2+9x+5

Solution for Y=-x^2+9x+5 equation:

=-Y^2+9Y+5

We move all terms to the left:

-(-Y^2+9Y+5)=0

We get rid of parentheses

Y^2-9Y-5=0

a = 1; b = -9; c = -5;
Δ = b2-4ac
Δ = -92-4·1·(-5)
Δ = 101
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{101}}{2*1}=\frac{9-\sqrt{101}}{2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{101}}{2*1}=\frac{9+\sqrt{101}}{2}
$