Y=-x^2+10x+30000

Solution for Y=-x^2+10x+30000 equation:

=-Y^2+10Y+30000

We move all terms to the left:

-(-Y^2+10Y+30000)=0

We get rid of parentheses

Y^2-10Y-30000=0

a = 1; b = -10; c = -30000;
Δ = b2-4ac
Δ = -102-4·1·(-30000)
Δ = 120100
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:

$\sqrt{\Delta}=\sqrt{120100}=\sqrt{100*1201}=\sqrt{100}*\sqrt{1201}=10\sqrt{1201}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{1201}}{2*1}=\frac{10-10\sqrt{1201}}{2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{1201}}{2*1}=\frac{10+10\sqrt{1201}}{2}
$