Y(x)=20x-2x^2

Solution for Y(x)=20x-2x^2 equation:

(Y)=20Y-2Y^2

We move all terms to the left:

(Y)-(20Y-2Y^2)=0

We get rid of parentheses

2Y^2-20Y+Y=0

We add all the numbers together, and all the variables

2Y^2-19Y=0

a = 2; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·2·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*2}=\frac{0}{4}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*2}=\frac{38}{4}
=9+1/2
$