w(3w-4)=119

Solution for w(3w-4)=119 equation:

w(3w-4)=119

We move all terms to the left:

w(3w-4)-(119)=0

We multiply parentheses

3w^2-4w-119=0

a = 3; b = -4; c = -119;
Δ = b2-4ac
Δ = -42-4·3·(-119)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-38}{2*3}=\frac{-34}{6}
=-5+2/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+38}{2*3}=\frac{42}{6}
=7
$