w(3w-4)=55

Solution for w(3w-4)=55 equation:

w(3w-4)=55

We move all terms to the left:

w(3w-4)-(55)=0

We multiply parentheses

3w^2-4w-55=0

a = 3; b = -4; c = -55;
Δ = b2-4ac
Δ = -42-4·3·(-55)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-26}{2*3}=\frac{-22}{6}
=-3+2/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+26}{2*3}=\frac{30}{6}
=5
$