0=2w^2-w-91

Solution for 0=2w^2-w-91 equation:

0=2w^2-w-91

We move all terms to the left:

0-(2w^2-w-91)=0

We add all the numbers together, and all the variables

-(2w^2-w-91)=0

We get rid of parentheses

-2w^2+w+91=0

a = -2; b = 1; c = +91;
Δ = b2-4ac
Δ = 12-4·(-2)·91
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-27}{2*-2}=\frac{-28}{-4}
=+7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+27}{2*-2}=\frac{26}{-4}
=-6+1/2
$