a(a+2)-(a+4)=100

Solution for a(a+2)-(a+4)=100 equation:

a(a+2)-(a+4)=100

We move all terms to the left:

a(a+2)-(a+4)-(100)=0

We multiply parentheses

a^2+2a-(a+4)-100=0

We get rid of parentheses

a^2+2a-a-4-100=0

We add all the numbers together, and all the variables

a^2+a-104=0

a = 1; b = 1; c = -104;
Δ = b2-4ac
Δ = 12-4·1·(-104)
Δ = 417
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{417}}{2*1}=\frac{-1-\sqrt{417}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{417}}{2*1}=\frac{-1+\sqrt{417}}{2}
$