x2-18x+81=2001

Solution for x2-18x+81=2001 equation:

x2-18x+81=2001

We move all terms to the left:

x2-18x+81-(2001)=0

We add all the numbers together, and all the variables

x^2-18x-1920=0

a = 1; b = -18; c = -1920;
Δ = b2-4ac
Δ = -182-4·1·(-1920)
Δ = 8004
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:

$\sqrt{\Delta}=\sqrt{8004}=\sqrt{4*2001}=\sqrt{4}*\sqrt{2001}=2\sqrt{2001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{2001}}{2*1}=\frac{18-2\sqrt{2001}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{2001}}{2*1}=\frac{18+2\sqrt{2001}}{2}
$