x^2-18x+81=x+3

Solution for x^2-18x+81=x+3 equation:

x^2-18x+81=x+3

We move all terms to the left:

x^2-18x+81-(x+3)=0

We get rid of parentheses

x^2-18x-x-3+81=0

We add all the numbers together, and all the variables

x^2-19x+78=0

a = 1; b = -19; c = +78;
Δ = b2-4ac
Δ = -192-4·1·78
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-7}{2*1}=\frac{12}{2}
=6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+7}{2*1}=\frac{26}{2}
=13
$