x^2-18x=81=0

Solution for x^2-18x=81=0 equation:

x^2-18x=81=0

We move all terms to the left:

x^2-18x-(81)=0

a = 1; b = -18; c = -81;
Δ = b2-4ac
Δ = -182-4·1·(-81)
Δ = 648
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18\sqrt{2}}{2*1}=\frac{18-18\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18\sqrt{2}}{2*1}=\frac{18+18\sqrt{2}}{2}
$