w(3w+5)=250

Solution for w(3w+5)=250 equation:

w(3w+5)=250

We move all terms to the left:

w(3w+5)-(250)=0

We multiply parentheses

3w^2+5w-250=0

a = 3; b = 5; c = -250;
Δ = b2-4ac
Δ = 52-4·3·(-250)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-55}{2*3}=\frac{-60}{6}
=-10
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+55}{2*3}=\frac{50}{6}
=8+1/3
$