0=2w^2-3w-65

Solution for 0=2w^2-3w-65 equation:

0=2w^2-3w-65

We move all terms to the left:

0-(2w^2-3w-65)=0

We add all the numbers together, and all the variables

-(2w^2-3w-65)=0

We get rid of parentheses

-2w^2+3w+65=0

a = -2; b = 3; c = +65;
Δ = b2-4ac
Δ = 32-4·(-2)·65
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-23}{2*-2}=\frac{-26}{-4}
=6+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+23}{2*-2}=\frac{20}{-4}
=-5
$