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

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

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

We add all the numbers together, and all the variables

(a+7)(-1a+7)=0

We multiply parentheses ..

(-1a^2+7a-7a+49)=0

We get rid of parentheses

-1a^2+7a-7a+49=0

We add all the numbers together, and all the variables

-1a^2+49=0

a = -1; b = 0; c = +49;
Δ = b2-4ac
Δ = 02-4·(-1)·49
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14}{2*-1}=\frac{-14}{-2}
=+7
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14}{2*-1}=\frac{14}{-2}
=-7
$