x2+1=x+23

Solution for x2+1=x+23 equation:

x2+1=x+23

We move all terms to the left:

x2+1-(x+23)=0

We add all the numbers together, and all the variables

x^2-(x+23)+1=0

We get rid of parentheses

x^2-x-23+1=0

We add all the numbers together, and all the variables

x^2-1x-22=0

a = 1; b = -1; c = -22;
Δ = b2-4ac
Δ = -12-4·1·(-22)
Δ = 89
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{-(-1)-\sqrt{89}}{2*1}=\frac{1-\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{89}}{2*1}=\frac{1+\sqrt{89}}{2}
$