(3+y)(8-y)=28

Solution for (3+y)(8-y)=28 equation:

(3+y)(8-y)=28

We move all terms to the left:

(3+y)(8-y)-(28)=0

We add all the numbers together, and all the variables

(y+3)(-1y+8)-28=0

We multiply parentheses ..

(-1y^2+8y-3y+24)-28=0

We get rid of parentheses

-1y^2+8y-3y+24-28=0

We add all the numbers together, and all the variables

-1y^2+5y-4=0

a = -1; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·(-1)·(-4)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3}{2*-1}=\frac{-8}{-2}
=+4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3}{2*-1}=\frac{-2}{-2}
=1
$