w(3w-5)=84

Solution for w(3w-5)=84 equation:

w(3w-5)=84

We move all terms to the left:

w(3w-5)-(84)=0

We multiply parentheses

3w^2-5w-84=0

a = 3; b = -5; c = -84;
Δ = b2-4ac
Δ = -52-4·3·(-84)
Δ = 1033
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{1033}}{2*3}=\frac{5-\sqrt{1033}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{1033}}{2*3}=\frac{5+\sqrt{1033}}{6}
$