Y=20x-44-2x^2

Solution for Y=20x-44-2x^2 equation:

=20Y-44-2Y^2

We move all terms to the left:

-(20Y-44-2Y^2)=0

We get rid of parentheses

2Y^2-20Y+44=0

a = 2; b = -20; c = +44;
Δ = b2-4ac
Δ = -202-4·2·44
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{3}}{2*2}=\frac{20-4\sqrt{3}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{3}}{2*2}=\frac{20+4\sqrt{3}}{4}
$