Y=-2x^2+80x+350

Solution for Y=-2x^2+80x+350 equation:

=-2Y^2+80Y+350

We move all terms to the left:

-(-2Y^2+80Y+350)=0

We get rid of parentheses

2Y^2-80Y-350=0

a = 2; b = -80; c = -350;
Δ = b2-4ac
Δ = -802-4·2·(-350)
Δ = 9200
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:

$\sqrt{\Delta}=\sqrt{9200}=\sqrt{400*23}=\sqrt{400}*\sqrt{23}=20\sqrt{23}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-20\sqrt{23}}{2*2}=\frac{80-20\sqrt{23}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+20\sqrt{23}}{2*2}=\frac{80+20\sqrt{23}}{4}
$