9y-y^2=5

Solution for 9y-y^2=5 equation:

9y-y^2=5

We move all terms to the left:

9y-y^2-(5)=0

We add all the numbers together, and all the variables

-1y^2+9y-5=0

a = -1; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·(-1)·(-5)
Δ = 61
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{61}}{2*-1}=\frac{-9-\sqrt{61}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{61}}{2*-1}=\frac{-9+\sqrt{61}}{-2}
$