w(3w+1)=154

Solution for w(3w+1)=154 equation:

w(3w+1)=154

We move all terms to the left:

w(3w+1)-(154)=0

We multiply parentheses

3w^2+w-154=0

a = 3; b = 1; c = -154;
Δ = b2-4ac
Δ = 12-4·3·(-154)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-43}{2*3}=\frac{-44}{6}
=-7+1/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+43}{2*3}=\frac{42}{6}
=7
$