0=-200x^2-2500x-900

Solution for 0=-200x^2-2500x-900 equation:

0=-200x^2-2500x-900

We move all terms to the left:

0-(-200x^2-2500x-900)=0

We add all the numbers together, and all the variables

-(-200x^2-2500x-900)=0

We get rid of parentheses

200x^2+2500x+900=0

a = 200; b = 2500; c = +900;
Δ = b2-4ac
Δ = 25002-4·200·900
Δ = 5530000
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:

$\sqrt{\Delta}=\sqrt{5530000}=\sqrt{10000*553}=\sqrt{10000}*\sqrt{553}=100\sqrt{553}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2500)-100\sqrt{553}}{2*200}=\frac{-2500-100\sqrt{553}}{400}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2500)+100\sqrt{553}}{2*200}=\frac{-2500+100\sqrt{553}}{400}
$