0=x^2+50x+200

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

0=x^2+50x+200

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-x^2-50x-200=0

We add all the numbers together, and all the variables

-1x^2-50x-200=0

a = -1; b = -50; c = -200;
Δ = b2-4ac
Δ = -502-4·(-1)·(-200)
Δ = 1700
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:

$\sqrt{\Delta}=\sqrt{1700}=\sqrt{100*17}=\sqrt{100}*\sqrt{17}=10\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{17}}{2*-1}=\frac{50-10\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{17}}{2*-1}=\frac{50+10\sqrt{17}}{-2}
$