0=x^2+200x+3500

Solution for 0=x^2+200x+3500 equation:

0=x^2+200x+3500

We move all terms to the left:

0-(x^2+200x+3500)=0

We add all the numbers together, and all the variables

-(x^2+200x+3500)=0

We get rid of parentheses

-x^2-200x-3500=0

We add all the numbers together, and all the variables

-1x^2-200x-3500=0

a = -1; b = -200; c = -3500;
Δ = b2-4ac
Δ = -2002-4·(-1)·(-3500)
Δ = 26000
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:

$\sqrt{\Delta}=\sqrt{26000}=\sqrt{400*65}=\sqrt{400}*\sqrt{65}=20\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-20\sqrt{65}}{2*-1}=\frac{200-20\sqrt{65}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+20\sqrt{65}}{2*-1}=\frac{200+20\sqrt{65}}{-2}
$