120000=-a^2+800a

Solution for 120000=-a^2+800a equation:

120000=-a^2+800a

We move all terms to the left:

120000-(-a^2+800a)=0

We get rid of parentheses

a^2-800a+120000=0

a = 1; b = -800; c = +120000;
Δ = b2-4ac
Δ = -8002-4·1·120000
Δ = 160000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{160000}=400$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-800)-400}{2*1}=\frac{400}{2}
=200
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-800)+400}{2*1}=\frac{1200}{2}
=600
$