(y+1)(y+8)=9

Solution for (y+1)(y+8)=9 equation:

(y+1)(y+8)=9

We move all terms to the left:

(y+1)(y+8)-(9)=0

We multiply parentheses ..

(+y^2+8y+y+8)-9=0

We get rid of parentheses

y^2+8y+y+8-9=0

We add all the numbers together, and all the variables

y^2+9y-1=0

a = 1; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·1·(-1)
Δ = 85
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{85}}{2*1}=\frac{-9-\sqrt{85}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{85}}{2*1}=\frac{-9+\sqrt{85}}{2}
$