w(3w-1)=520

Solution for w(3w-1)=520 equation:

w(3w-1)=520

We move all terms to the left:

w(3w-1)-(520)=0

We multiply parentheses

3w^2-1w-520=0

a = 3; b = -1; c = -520;
Δ = b2-4ac
Δ = -12-4·3·(-520)
Δ = 6241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6241}=79$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-79}{2*3}=\frac{-78}{6}
=-13
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+79}{2*3}=\frac{80}{6}
=13+1/3
$