5000=w^2+50w+600

Solution for 5000=w^2+50w+600 equation:

5000=w^2+50w+600

We move all terms to the left:

5000-(w^2+50w+600)=0

We get rid of parentheses

-w^2-50w-600+5000=0

We add all the numbers together, and all the variables

-1w^2-50w+4400=0

a = -1; b = -50; c = +4400;
Δ = b2-4ac
Δ = -502-4·(-1)·4400
Δ = 20100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20100}=\sqrt{100*201}=\sqrt{100}*\sqrt{201}=10\sqrt{201}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{201}}{2*-1}=\frac{50-10\sqrt{201}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{201}}{2*-1}=\frac{50+10\sqrt{201}}{-2}
$