(a-7)(a+12)=0

Solution for (a-7)(a+12)=0 equation:

(a-7)(a+12)=0

We multiply parentheses ..

(+a^2+12a-7a-84)=0

We get rid of parentheses

a^2+12a-7a-84=0

We add all the numbers together, and all the variables

a^2+5a-84=0

a = 1; b = 5; c = -84;
Δ = b2-4ac
Δ = 52-4·1·(-84)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-19}{2*1}=\frac{-24}{2}
=-12
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*1}=\frac{14}{2}
=7
$