(y-4)(y+6)-(-2)2=8

Solution for (y-4)(y+6)-(-2)2=8 equation:

(y-4)(y+6)-(-2)2=8

We move all terms to the left:

(y-4)(y+6)-(-2)2-(8)=0

determiningTheFunctionDomain
(y-4)(y+6)-8-(-2)2=0

We add all the numbers together, and all the variables

(y-4)(y+6)-4=0

We multiply parentheses ..

(+y^2+6y-4y-24)-4=0

We get rid of parentheses

y^2+6y-4y-24-4=0

We add all the numbers together, and all the variables

y^2+2y-28=0

a = 1; b = 2; c = -28;
Δ = b2-4ac
Δ = 22-4·1·(-28)
Δ = 116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{29}}{2*1}=\frac{-2-2\sqrt{29}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{29}}{2*1}=\frac{-2+2\sqrt{29}}{2}
$