0=-20x^2-50x+200

Solution for 0=-20x^2-50x+200 equation:

0=-20x^2-50x+200

We move all terms to the left:

0-(-20x^2-50x+200)=0

We add all the numbers together, and all the variables

-(-20x^2-50x+200)=0

We get rid of parentheses

20x^2+50x-200=0

a = 20; b = 50; c = -200;
Δ = b2-4ac
Δ = 502-4·20·(-200)
Δ = 18500
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:

$\sqrt{\Delta}=\sqrt{18500}=\sqrt{100*185}=\sqrt{100}*\sqrt{185}=10\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-10\sqrt{185}}{2*20}=\frac{-50-10\sqrt{185}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+10\sqrt{185}}{2*20}=\frac{-50+10\sqrt{185}}{40}
$