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

Solution for (2+y)(8-y)=9 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

(y+2)(-1y+8)-9=0

We multiply parentheses ..

(-1y^2+8y-2y+16)-9=0

We get rid of parentheses

-1y^2+8y-2y+16-9=0

We add all the numbers together, and all the variables

-1y^2+6y+7=0

a = -1; b = 6; c = +7;
Δ = b2-4ac
Δ = 62-4·(-1)·7
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-8}{2*-1}=\frac{-14}{-2}
=+7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+8}{2*-1}=\frac{2}{-2}
=-1
$