Y=-5x^2+20x+60

Solution for Y=-5x^2+20x+60 equation:

=-5Y^2+20Y+60

We move all terms to the left:

-(-5Y^2+20Y+60)=0

We get rid of parentheses

5Y^2-20Y-60=0

a = 5; b = -20; c = -60;
Δ = b2-4ac
Δ = -202-4·5·(-60)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-40}{2*5}=\frac{-20}{10}
=-2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+40}{2*5}=\frac{60}{10}
=6
$