(a+5)(a+3)=80

Solution for (a+5)(a+3)=80 equation:

(a+5)(a+3)=80

We move all terms to the left:

(a+5)(a+3)-(80)=0

We multiply parentheses ..

(+a^2+3a+5a+15)-80=0

We get rid of parentheses

a^2+3a+5a+15-80=0

We add all the numbers together, and all the variables

a^2+8a-65=0

a = 1; b = 8; c = -65;
Δ = b2-4ac
Δ = 82-4·1·(-65)
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{-(8)-18}{2*1}=\frac{-26}{2}
=-13
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+18}{2*1}=\frac{10}{2}
=5
$