(y+2)(y-4)=7

Solution for (y+2)(y-4)=7 equation:

(y+2)(y-4)=7

We move all terms to the left:

(y+2)(y-4)-(7)=0

We multiply parentheses ..

(+y^2-4y+2y-8)-7=0

We get rid of parentheses

y^2-4y+2y-8-7=0

We add all the numbers together, and all the variables

y^2-2y-15=0

a = 1; b = -2; c = -15;
Δ = b2-4ac
Δ = -22-4·1·(-15)
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{-(-2)-8}{2*1}=\frac{-6}{2}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8}{2*1}=\frac{10}{2}
=5
$