(a-100)*(a/100)=200

Solution for (a-100)*(a/100)=200 equation:

(a-100)(a/100)=200

We move all terms to the left:

(a-100)(a/100)-(200)=0

We add all the numbers together, and all the variables

(a-100)(+a/100)-200=0

We multiply parentheses ..

(+a^2-100a)-200=0

We get rid of parentheses

a^2-100a-200=0

a = 1; b = -100; c = -200;
Δ = b2-4ac
Δ = -1002-4·1·(-200)
Δ = 10800
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:

$\sqrt{\Delta}=\sqrt{10800}=\sqrt{3600*3}=\sqrt{3600}*\sqrt{3}=60\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-60\sqrt{3}}{2*1}=\frac{100-60\sqrt{3}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+60\sqrt{3}}{2*1}=\frac{100+60\sqrt{3}}{2}
$