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

We get rid of parentheses

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}
$