5000=200+b2

Solution for 5000=200+b2 equation:

5000=200+b2

We move all terms to the left:

5000-(200+b2)=0

We add all the numbers together, and all the variables

-(+b^2+200)+5000=0

We get rid of parentheses

-b^2-200+5000=0

We add all the numbers together, and all the variables

-1b^2+4800=0

a = -1; b = 0; c = +4800;
Δ = b2-4ac
Δ = 02-4·(-1)·4800
Δ = 19200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{19200}=\sqrt{6400*3}=\sqrt{6400}*\sqrt{3}=80\sqrt{3}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{3}}{2*-1}=\frac{0-80\sqrt{3}}{-2}
=-\frac{80\sqrt{3}}{-2}
=-\frac{40\sqrt{3}}{-1}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{3}}{2*-1}=\frac{0+80\sqrt{3}}{-2}
=\frac{80\sqrt{3}}{-2}
=\frac{40\sqrt{3}}{-1}
$