Y=100x-2x^2

Solution for Y=100x-2x^2 equation:

=100Y-2Y^2

We move all terms to the left:

-(100Y-2Y^2)=0

We get rid of parentheses

2Y^2-100Y=0

a = 2; b = -100; c = 0;
Δ = b2-4ac
Δ = -1002-4·2·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-100}{2*2}=\frac{0}{4}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+100}{2*2}=\frac{200}{4}
=50
$