Y=-40x+2x^2-2x

Solution for Y=-40x+2x^2-2x equation:

=-40Y+2Y^2-2Y

We move all terms to the left:

-(-40Y+2Y^2-2Y)=0

We get rid of parentheses

-2Y^2+40Y+2Y=0

We add all the numbers together, and all the variables

-2Y^2+42Y=0

a = -2; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·(-2)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42}{2*-2}=\frac{-84}{-4}
=+21
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*-2}=\frac{0}{-4}
=0
$