-5x+19=x^2+1

Solution for -5x+19=x^2+1 equation:

-5x+19=x^2+1

We move all terms to the left:

-5x+19-(x^2+1)=0

We get rid of parentheses

-x^2-5x-1+19=0

We add all the numbers together, and all the variables

-1x^2-5x+18=0

a = -1; b = -5; c = +18;
Δ = b2-4ac
Δ = -52-4·(-1)·18
Δ = 97
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{-(-5)-\sqrt{97}}{2*-1}=\frac{5-\sqrt{97}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{97}}{2*-1}=\frac{5+\sqrt{97}}{-2}
$