5000=(30w+20)(w)

Solution for 5000=(30w+20)(w) equation:

5000=(30w+20)(w)

We move all terms to the left:

5000-((30w+20)(w))=0


We calculate terms in parentheses: -((30w+20)w), so:

(30w+20)w

We multiply parentheses

30w^2+20w

Back to the equation:

-(30w^2+20w)


We get rid of parentheses

-30w^2-20w+5000=0

a = -30; b = -20; c = +5000;
Δ = b2-4ac
Δ = -202-4·(-30)·5000
Δ = 600400
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:

$\sqrt{\Delta}=\sqrt{600400}=\sqrt{400*1501}=\sqrt{400}*\sqrt{1501}=20\sqrt{1501}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{1501}}{2*-30}=\frac{20-20\sqrt{1501}}{-60}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{1501}}{2*-30}=\frac{20+20\sqrt{1501}}{-60}
$