(-y^2)+1200y-400=0

Solution for (-y^2)+1200y-400=0 equation:

(-y^2)+1200y-400=0

We get rid of parentheses

-y^2+1200y-400=0

We add all the numbers together, and all the variables

-1y^2+1200y-400=0

a = -1; b = 1200; c = -400;
Δ = b2-4ac
Δ = 12002-4·(-1)·(-400)
Δ = 1438400
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:

$\sqrt{\Delta}=\sqrt{1438400}=\sqrt{1600*899}=\sqrt{1600}*\sqrt{899}=40\sqrt{899}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1200)-40\sqrt{899}}{2*-1}=\frac{-1200-40\sqrt{899}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1200)+40\sqrt{899}}{2*-1}=\frac{-1200+40\sqrt{899}}{-2}
$