Y=-2x^2+60x-350

Solution for Y=-2x^2+60x-350 equation:

=-2Y^2+60Y-350

We move all terms to the left:

-(-2Y^2+60Y-350)=0

We get rid of parentheses

2Y^2-60Y+350=0

a = 2; b = -60; c = +350;
Δ = b2-4ac
Δ = -602-4·2·350
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-20\sqrt{2}}{2*2}=\frac{60-20\sqrt{2}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+20\sqrt{2}}{2*2}=\frac{60+20\sqrt{2}}{4}
$