w^2-18w-81=12

Solution for w^2-18w-81=12 equation:

w^2-18w-81=12

We move all terms to the left:

w^2-18w-81-(12)=0

We add all the numbers together, and all the variables

w^2-18w-93=0

a = 1; b = -18; c = -93;
Δ = b2-4ac
Δ = -182-4·1·(-93)
Δ = 696
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{696}=\sqrt{4*174}=\sqrt{4}*\sqrt{174}=2\sqrt{174}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{174}}{2*1}=\frac{18-2\sqrt{174}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{174}}{2*1}=\frac{18+2\sqrt{174}}{2}
$