w^2-81w+81=0

Solution for w^2-81w+81=0 equation:

w^2-81w+81=0

a = 1; b = -81; c = +81;
Δ = b2-4ac
Δ = -812-4·1·81
Δ = 6237
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:

$\sqrt{\Delta}=\sqrt{6237}=\sqrt{81*77}=\sqrt{81}*\sqrt{77}=9\sqrt{77}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-9\sqrt{77}}{2*1}=\frac{81-9\sqrt{77}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+9\sqrt{77}}{2*1}=\frac{81+9\sqrt{77}}{2}
$