(3+w)w=270

Solution for (3+w)w=270 equation:

(3+w)w=270

We move all terms to the left:

(3+w)w-(270)=0

We add all the numbers together, and all the variables

(w+3)w-270=0

We multiply parentheses

w^2+3w-270=0

a = 1; b = 3; c = -270;
Δ = b2-4ac
Δ = 32-4·1·(-270)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-33}{2*1}=\frac{-36}{2}
=-18
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+33}{2*1}=\frac{30}{2}
=15
$