x2-18x+81=24

Solution for x2-18x+81=24 equation:

x2-18x+81=24

We move all terms to the left:

x2-18x+81-(24)=0

We add all the numbers together, and all the variables

x^2-18x+57=0

a = 1; b = -18; c = +57;
Δ = b2-4ac
Δ = -182-4·1·57
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{6}}{2*1}=\frac{18-4\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{6}}{2*1}=\frac{18+4\sqrt{6}}{2}
$