(20a)(100-20a)=900

Solution for (20a)(100-20a)=900 equation:

(20a)(100-20a)=900

We move all terms to the left:

(20a)(100-20a)-(900)=0

We add all the numbers together, and all the variables

20a(-20a+100)-900=0

We multiply parentheses

-400a^2+2000a-900=0

a = -400; b = 2000; c = -900;
Δ = b2-4ac
Δ = 20002-4·(-400)·(-900)
Δ = 2560000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2560000}=1600$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2000)-1600}{2*-400}=\frac{-3600}{-800}
=4+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2000)+1600}{2*-400}=\frac{-400}{-800}
=1/2
$