Y=-5x^2+600x

Solution for Y=-5x^2+600x equation:

=-5Y^2+600Y

We move all terms to the left:

-(-5Y^2+600Y)=0

We get rid of parentheses

5Y^2-600Y=0

a = 5; b = -600; c = 0;
Δ = b2-4ac
Δ = -6002-4·5·0
Δ = 360000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{360000}=600$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-600}{2*5}=\frac{0}{10}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+600}{2*5}=\frac{1200}{10}
=120
$