x^2-18x+81=455

Solution for x^2-18x+81=455 equation:

x^2-18x+81=455

We move all terms to the left:

x^2-18x+81-(455)=0

We add all the numbers together, and all the variables

x^2-18x-374=0

a = 1; b = -18; c = -374;
Δ = b2-4ac
Δ = -182-4·1·(-374)
Δ = 1820
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:

$\sqrt{\Delta}=\sqrt{1820}=\sqrt{4*455}=\sqrt{4}*\sqrt{455}=2\sqrt{455}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{455}}{2*1}=\frac{18-2\sqrt{455}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{455}}{2*1}=\frac{18+2\sqrt{455}}{2}
$