0=2w^2-5w-33

Solution for 0=2w^2-5w-33 equation:

0=2w^2-5w-33

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of 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
$