Y=400x-x^2

Solution for Y=400x-x^2 equation:

=400Y-Y^2

We move all terms to the left:

-(400Y-Y^2)=0

We get rid of parentheses

Y^2-400Y=0

a = 1; b = -400; c = 0;
Δ = b2-4ac
Δ = -4002-4·1·0
Δ = 160000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{160000}=400$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-400}{2*1}=\frac{0}{2}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+400}{2*1}=\frac{800}{2}
=400
$