Y=-2x^2+28x-97

Solution for Y=-2x^2+28x-97 equation:

=-2Y^2+28Y-97

We move all terms to the left:

-(-2Y^2+28Y-97)=0

We get rid of parentheses

2Y^2-28Y+97=0

a = 2; b = -28; c = +97;
Δ = b2-4ac
Δ = -282-4·2·97
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{2}}{2*2}=\frac{28-2\sqrt{2}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{2}}{2*2}=\frac{28+2\sqrt{2}}{4}
$