Y=-20x^2+1114x-9010

Solution for Y=-20x^2+1114x-9010 equation:

=-20Y^2+1114Y-9010

We move all terms to the left:

-(-20Y^2+1114Y-9010)=0

We get rid of parentheses

20Y^2-1114Y+9010=0

a = 20; b = -1114; c = +9010;
Δ = b2-4ac
Δ = -11142-4·20·9010
Δ = 520196
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:

$\sqrt{\Delta}=\sqrt{520196}=\sqrt{4*130049}=\sqrt{4}*\sqrt{130049}=2\sqrt{130049}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1114)-2\sqrt{130049}}{2*20}=\frac{1114-2\sqrt{130049}}{40}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1114)+2\sqrt{130049}}{2*20}=\frac{1114+2\sqrt{130049}}{40}
$