x2=19x+1

Solution for x2=19x+1 equation:

x2=19x+1

We move all terms to the left:

x2-(19x+1)=0

We add all the numbers together, and all the variables

x^2-(19x+1)=0

We get rid of parentheses

x^2-19x-1=0

a = 1; b = -19; c = -1;
Δ = b2-4ac
Δ = -192-4·1·(-1)
Δ = 365
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{365}}{2*1}=\frac{19-\sqrt{365}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{365}}{2*1}=\frac{19+\sqrt{365}}{2}
$