2w^2-w=66

Solution for 2w^2-w=66 equation:

2w^2-w=66

We move all terms to the left:

2w^2-w-(66)=0

We add all the numbers together, and all the variables

2w^2-1w-66=0

a = 2; b = -1; c = -66;
Δ = b2-4ac
Δ = -12-4·2·(-66)
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{-(-1)-23}{2*2}=\frac{-22}{4}
=-5+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+23}{2*2}=\frac{24}{4}
=6
$