x2=18x+1

Solution for x2=18x+1 equation:

x2=18x+1

We move all terms to the left:

x2-(18x+1)=0

We add all the numbers together, and all the variables

x^2-(18x+1)=0

We get rid of parentheses

x^2-18x-1=0

a = 1; b = -18; c = -1;
Δ = b2-4ac
Δ = -182-4·1·(-1)
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{82}}{2*1}=\frac{18-2\sqrt{82}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{82}}{2*1}=\frac{18+2\sqrt{82}}{2}
$