50w+w^2=5000

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

50w+w^2=5000

We move all terms to the left:

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

a = 1; b = 50; c = -5000;
Δ = b2-4ac
Δ = 502-4·1·(-5000)
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-150}{2*1}=\frac{-200}{2}
=-100
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+150}{2*1}=\frac{100}{2}
=50
$