(3w-1)w=200

Solution for (3w-1)w=200 equation:

(3w-1)w=200

We move all terms to the left:

(3w-1)w-(200)=0

We multiply parentheses

3w^2-1w-200=0

a = 3; b = -1; c = -200;
Δ = b2-4ac
Δ = -12-4·3·(-200)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-49}{2*3}=\frac{-48}{6}
=-8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+49}{2*3}=\frac{50}{6}
=8+1/3
$