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

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

=-2Y^2+2Y+60

We move all terms to the left:

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

We get rid of parentheses

2Y^2-2Y-60=0

a = 2; b = -2; c = -60;
Δ = b2-4ac
Δ = -22-4·2·(-60)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-22}{2*2}=\frac{-20}{4}
=-5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+22}{2*2}=\frac{24}{4}
=6
$