u^2=18u+81

Solution for u^2=18u+81 equation:

u^2=18u+81

We move all terms to the left:

u^2-(18u+81)=0

We get rid of parentheses

u^2-18u-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:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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