(y+4)(y+2)=24

Solution for (y+4)(y+2)=24 equation:

(y+4)(y+2)=24

We move all terms to the left:

(y+4)(y+2)-(24)=0

We multiply parentheses ..

(+y^2+2y+4y+8)-24=0

We get rid of parentheses

y^2+2y+4y+8-24=0

We add all the numbers together, and all the variables

y^2+6y-16=0

a = 1; b = 6; c = -16;
Δ = b2-4ac
Δ = 62-4·1·(-16)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10}{2*1}=\frac{-16}{2}
=-8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10}{2*1}=\frac{4}{2}
=2
$