w^2+30w-5000=0

Solution for w^2+30w-5000=0 equation:

w^2+30w-5000=0

a = 1; b = 30; c = -5000;
Δ = b2-4ac
Δ = 302-4·1·(-5000)
Δ = 20900
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:

$\sqrt{\Delta}=\sqrt{20900}=\sqrt{100*209}=\sqrt{100}*\sqrt{209}=10\sqrt{209}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{209}}{2*1}=\frac{-30-10\sqrt{209}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{209}}{2*1}=\frac{-30+10\sqrt{209}}{2}
$