Y=-20x^2+320x-780

Solution for Y=-20x^2+320x-780 equation:

=-20Y^2+320Y-780

We move all terms to the left:

-(-20Y^2+320Y-780)=0

We get rid of parentheses

20Y^2-320Y+780=0

a = 20; b = -320; c = +780;
Δ = b2-4ac
Δ = -3202-4·20·780
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-200}{2*20}=\frac{120}{40}
=3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+200}{2*20}=\frac{520}{40}
=13
$