0=-16x^2+600x-400

Solution for 0=-16x^2+600x-400 equation:

0=-16x^2+600x-400

We move all terms to the left:

0-(-16x^2+600x-400)=0

We add all the numbers together, and all the variables

-(-16x^2+600x-400)=0

We get rid of parentheses

16x^2-600x+400=0

a = 16; b = -600; c = +400;
Δ = b2-4ac
Δ = -6002-4·16·400
Δ = 334400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{334400}=\sqrt{1600*209}=\sqrt{1600}*\sqrt{209}=40\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-40\sqrt{209}}{2*16}=\frac{600-40\sqrt{209}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+40\sqrt{209}}{2*16}=\frac{600+40\sqrt{209}}{32}
$