9=5+17y-16y^2

Solution for 9=5+17y-16y^2 equation:

9=5+17y-16y^2

We move all terms to the left:

9-(5+17y-16y^2)=0

We get rid of parentheses

16y^2-17y-5+9=0

We add all the numbers together, and all the variables

16y^2-17y+4=0

a = 16; b = -17; c = +4;
Δ = b2-4ac
Δ = -172-4·16·4
Δ = 33
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{-(-17)-\sqrt{33}}{2*16}=\frac{17-\sqrt{33}}{32}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{33}}{2*16}=\frac{17+\sqrt{33}}{32}
$