(a+2)a=10^2

Solution for (a+2)a=10^2 equation:

(a+2)a=10^2

We move all terms to the left:

(a+2)a-(10^2)=0

We add all the numbers together, and all the variables

(a+2)a-100=0

We multiply parentheses

a^2+2a-100=0

a = 1; b = 2; c = -100;
Δ = b2-4ac
Δ = 22-4·1·(-100)
Δ = 404
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{101}}{2*1}=\frac{-2-2\sqrt{101}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{101}}{2*1}=\frac{-2+2\sqrt{101}}{2}
$