27w-w^2-164=0

Solution for 27w-w^2-164=0 equation:

27w-w^2-164=0

We add all the numbers together, and all the variables

-1w^2+27w-164=0

a = -1; b = 27; c = -164;
Δ = b2-4ac
Δ = 272-4·(-1)·(-164)
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-\sqrt{73}}{2*-1}=\frac{-27-\sqrt{73}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{73}}{2*-1}=\frac{-27+\sqrt{73}}{-2}
$