a(2+a)=99

Solution for a(2+a)=99 equation:

a(2+a)=99

We move all terms to the left:

a(2+a)-(99)=0

We add all the numbers together, and all the variables

a(a+2)-99=0

We multiply parentheses

a^2+2a-99=0

a = 1; b = 2; c = -99;
Δ = b2-4ac
Δ = 22-4·1·(-99)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-20}{2*1}=\frac{-22}{2}
=-11
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+20}{2*1}=\frac{18}{2}
=9
$