w(3w+7)=150

Solution for w(3w+7)=150 equation:

w(3w+7)=150

We move all terms to the left:

w(3w+7)-(150)=0

We multiply parentheses

3w^2+7w-150=0

a = 3; b = 7; c = -150;
Δ = b2-4ac
Δ = 72-4·3·(-150)
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{-(7)-43}{2*3}=\frac{-50}{6}
=-8+1/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+43}{2*3}=\frac{36}{6}
=6
$