-y^2+9y+45=0

Solution for -y^2+9y+45=0 equation:

-y^2+9y+45=0

We add all the numbers together, and all the variables

-1y^2+9y+45=0

a = -1; b = 9; c = +45;
Δ = b2-4ac
Δ = 92-4·(-1)·45
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{29}}{2*-1}=\frac{-9-3\sqrt{29}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{29}}{2*-1}=\frac{-9+3\sqrt{29}}{-2}
$