(a+4)*(a-2)=72

Solution for (a+4)*(a-2)=72 equation:

(a+4)(a-2)=72

We move all terms to the left:

(a+4)(a-2)-(72)=0

We multiply parentheses ..

(+a^2-2a+4a-8)-72=0

We get rid of parentheses

a^2-2a+4a-8-72=0

We add all the numbers together, and all the variables

a^2+2a-80=0

a = 1; b = 2; c = -80;
Δ = b2-4ac
Δ = 22-4·1·(-80)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-18}{2*1}=\frac{-20}{2}
=-10
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+18}{2*1}=\frac{16}{2}
=8
$