(2w+5)w=33

Solution for (2w+5)w=33 equation:

(2w+5)w=33

We move all terms to the left:

(2w+5)w-(33)=0

We multiply parentheses

2w^2+5w-33=0

a = 2; b = 5; c = -33;
Δ = b2-4ac
Δ = 52-4·2·(-33)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-17}{2*2}=\frac{-22}{4}
=-5+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+17}{2*2}=\frac{12}{4}
=3
$