3w(820-6w/6)=16500

Solution for 3w(820-6w/6)=16500 equation:

3w(820-6w/6)=16500

We move all terms to the left:

3w(820-6w/6)-(16500)=0

We add all the numbers together, and all the variables

3w(-6w/6+820)-16500=0

We multiply parentheses

-18w^2+2460w-16500=0

a = -18; b = 2460; c = -16500;
Δ = b2-4ac
Δ = 24602-4·(-18)·(-16500)
Δ = 4863600
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:

$\sqrt{\Delta}=\sqrt{4863600}=\sqrt{3600*1351}=\sqrt{3600}*\sqrt{1351}=60\sqrt{1351}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2460)-60\sqrt{1351}}{2*-18}=\frac{-2460-60\sqrt{1351}}{-36}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2460)+60\sqrt{1351}}{2*-18}=\frac{-2460+60\sqrt{1351}}{-36}
$